Journal of Graph Theory最新文献_第8页

Refining Tree-Decompositions so That They Display the k-Blocks 改进树分解，使它们显示k块

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-02-10 DOI: 10.1002/jgt.23230

Sandra Albrechtsen

Carmesin and Gollin proved that every finite graph has a canonical tree-decomposition $� � � � � � (� � � T � �, � � V � � �) � � � �$ of adhesion less than $� � � � � k � � �$ that efficiently distinguishes every two distinct $� � � � � k � � �$ -profiles, and which has the further property that every separable $� � � � � k � � �$ -block is equal to the unique part of $� � � � � � (� � � T � �, � � V � � �) � � � �$ in which it is contained. We give a shorter proof of this result by showing that such a tree-decomposition can in fact be obtained from any canonical tight tree-decomposition of adhesion less than $� � � � � k � � �$ . For this, we decompose the parts of such a tree-decomposition by further tree-decompositions. As an application, we also obtain a generalization of Carmesin and Gollin's result to locally finite graphs.

Carmesin和Gollin证明了每个有限图都有一个正则树分解(T，V)的附着力小于k，有效地区分每两个不同的k - 概要文件,它还有一个进一步的性质，即每一个可分离的k块都等于(T)的唯一部分， V)它被包含在其中。我们通过证明这样的树分解实际上可以从任何小于k的附着力正则紧树分解中得到，从而给出了这个结果的一个简短的证明。为此，我们通过进一步的树分解来分解这种树分解的各个部分。作为应用，我们也得到了Carmesin和Gollin结果在局部有限图上的推广。

{"title":"Refining Tree-Decompositions so That They Display the k-Blocks","authors":"Sandra Albrechtsen","doi":"10.1002/jgt.23230","DOIUrl":"https://doi.org/10.1002/jgt.23230","url":null,"abstract":"Carmesin and Gollin proved that every finite graph has a canonical tree-decomposition <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>V</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of adhesion less than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> that efficiently distinguishes every two distinct <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-profiles, and which has the further property that every separable <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-block is equal to the unique part of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>T</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>V</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in which it is contained. We give a shorter proof of this result by showing that such a tree-decomposition can in fact be obtained from any canonical tight tree-decomposition of adhesion less than <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. For this, we decompose the parts of such a tree-decomposition by further tree-decompositions. As an application, we also obtain a generalization of Carmesin and Gollin's result to locally finite graphs.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 3","pages":"310-314"},"PeriodicalIF":0.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23230","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Independent Sets of Random Trees and Sparse Random Graphs 随机树和稀疏随机图的独立集

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-02-10 DOI: 10.1002/jgt.23225

Steven Heilman

An independent set of size $� � � � � k � � �$ in a finite undirected graph $� � � � � G � � �$ is a set of $� � � � � k � � �$ vertices of the graph, no two of which are connected by an edge. Let $� � � � � �_{x � � k �} � � � (� � G � �) � � � �$ be the number of independent sets of size $� � � � � k � � �$ in the graph $� � � � � G � � �$ and let $� � � � � α � � � (� � G � �) � � � = � � \max � � � {� � � k � � \geq � � 0 � �$

有限无向图G中大小为k的独立集是k的集合图的顶点，其中没有两个被一条边连接。设x k (G)为图G中大小为k的独立集合，设α(G) = max {k≥0 :x k (G)≠0}。1987年，阿拉维，马尔德，施文克，Erdős询问独立集合序列x 0 (G)， x1 (G)，... ,x α (G)(G)是单峰的（序列先上升后下降）。这个问题仍然悬而未决。2006年，Levit和Mandrescu证明了树的独立集合序列的最后三分之一是递减的。我们展示了前46个。随机树中8%的独立集合序列随着顶点数量趋于无穷而呈（指数）高概率增长。所以，关于Alavi， Malde， Schwenk和Erdős的问题有“五分之四正确”的高概率。我们还展示了Erdős-Rényi随机图的独立集合序列的单模性，当单个顶点的期望程度很大时（随着图中顶点的数量趋于无穷，除了模态附近的一个小区域外，具有[指数]高概率）。对于随机正则图，给出了较弱的结果。大小为k的独立集合随k变化的结构在概率、统计物理、组合学和计算机科学中都很有趣。

{"title":"Independent Sets of Random Trees and Sparse Random Graphs","authors":"Steven Heilman","doi":"10.1002/jgt.23225","DOIUrl":"https://doi.org/10.1002/jgt.23225","url":null,"abstract":"An independent set of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in a finite undirected graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> vertices of the graph, no two of which are connected by an edge. Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>x</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be the number of independent sets of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> in the graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>α</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>max</mi>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>0</mn>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 3","pages":"294-309"},"PeriodicalIF":0.9,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23225","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Directed Graphs Without Rainbow Triangles 没有彩虹三角形的有向图

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-02-04 DOI: 10.1002/jgt.23224

Sebastian Babiński, Andrzej Grzesik, Magdalena Prorok

One of the most fundamental results in graph theory is Mantel's theorem which determines the maximum number of edges in a triangle-free graph of order

� � �                  � � n � � �

. Recently, a colorful variant of this problem has been solved. In this variant we consider

� � �                  � � c � � �

graphs on a common vertex set, think of each graph as edges in a distinct color, and want to determine the smallest number of edges in each color which guarantees the existence of a rainbow triangle. Here, we solve the analogous problem for directed graphs without rainbow triangles, either directed or transitive, for any number of colors. The constructions and proofs essentially differ for

� � �                  � � c �                     � = �                     � 3 � � �

and

� � �                  � � c �                     � \geq �                     � 4 � � �

and the type of the forbidden triangle. Additionally, we also solve the analogous problem in the setting of oriented graphs.

图论中最基本的结果之一是曼特尔定理，它决定了n阶无三角形图的最大边数。最近，这个问题的一个不同版本得到了解决。在这种变体中，我们考虑一个公共顶点集上的c个图，将每个图视为具有不同颜色的边，并想要确定每种颜色中保证彩虹三角形存在的最小边数。在这里，我们解决了无彩虹三角形的有向图的类似问题，无论彩虹三角形是有向的还是可传递的，对于任意数量的颜色。c = 3和c≥4的构造和证明本质上是不同的禁止三角形的类型。此外，我们还解决了有向图设置中的类似问题。

{"title":"Directed Graphs Without Rainbow Triangles","authors":"Sebastian Babiński, Andrzej Grzesik, Magdalena Prorok","doi":"10.1002/jgt.23224","DOIUrl":"https://doi.org/10.1002/jgt.23224","url":null,"abstract":"<div>\u0000 \u0000 One of the most fundamental results in graph theory is Mantel's theorem which determines the maximum number of edges in a triangle-free graph of order <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. Recently, a colorful variant of this problem has been solved. In this variant we consider <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> graphs on a common vertex set, think of each graph as edges in a distinct color, and want to determine the smallest number of edges in each color which guarantees the existence of a rainbow triangle. Here, we solve the analogous problem for directed graphs without rainbow triangles, either directed or transitive, for any number of colors. The constructions and proofs essentially differ for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>c</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>4</mn>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and the type of the forbidden triangle. Additionally, we also solve the analogous problem in the setting of oriented graphs.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 3","pages":"269-281"},"PeriodicalIF":0.9,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Polynomial Characterizations of Distance-Biregular Graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-02-04 DOI: 10.1002/jgt.23227

Sabrina Lato

Fiol, Garriga, and Yebra introduced the notion of pseudo-distance-regular vertices, which they used to come up with a new characterization of distance-regular graphs. Building on that work, Fiol and Garriga developed the spectral excess theorem for distance-regular graphs. We extend both these characterizations to distance-biregular graphs and show how these characterizations can be used to study bipartite graphs with distance-regular halved graphs and graphs with the spectrum of a distance-biregular graph.

Fiol， Garriga和Yebra引入了伪距离规则顶点的概念，他们利用这个概念提出了距离规则图的一个新的表征。在此基础上，Fiol和Garriga提出了距离正则图的谱过剩定理。我们将这两种表征推广到距离双正则图，并展示了如何将这些表征用于研究具有距离正则半图的二部图和具有距离双正则图谱的图。

引用次数: 0

Extremal Results on Conflict-Free Coloring

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-24 DOI: 10.1002/jgt.23223

Sriram Bhyravarapu, Shiwali Gupta, Subrahmanyam Kalyanasundaram, Rogers Mathew

<div> A conflict-free open neighborhood (CFON) coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph <math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math>, the smallest number of colors required for such a coloring is called the CFON chromatic number and is denoted by <math> <semantics> <mrow> <mrow> <msub> <mi>χ</mi> <mi>ON</mi> </msub> <mrow> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math>. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free (CF) closed neighborhood (CFCN) coloring, and CFCN chromatic number (denoted by <math> <semantics> <mrow> <mrow> <msub> <mi>χ</mi> <mi>CN</mi> </msub> <mrow> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math>). The notion of CF coloring was introduced in 2002, and has since received considerable attention. We study CFON and CFCN colorings and show the following results. In what follows, <math> <semantics> <mrow> <mrow> <mi>Δ</mi> </mrow> </mrow> </semantics></math> denotes the maximum degree of the graph. <ul> <li> We show that if <math> <semantics> <mrow> <mrow> <mi>G</mi> </mrow> </mrow> </semantics></math> is a <math> <semantics> <mrow> <mrow> <msub> <mi>K</mi>

Dębski和Przybyło已经证明，如果G是一个线形图，则χ CN (G)= 0 (ln Δ) .作为一个开放的问题，他们问他们的结果是否可以推广到无爪（k1），3 -free)图，它是线形图的超类。自χ CN (G)≤2 χ on (g)，我们的结果回答了他们的开放性问题。已知k1存在独立的家族。 k个有χ ON的自由图(G) = Ω (lnΔ)和χ ON(g) = Ω (K)。对于k1，k自由图n 顶点,我们证明了χ CN (G) = 0 (lnklnn)。很容易看出，f CN (δ’)≥f CN（δ）当δ′ & lt;δ .设c为正常数。结果表明，fcn (cΔ) = Θ (lnΔ)。

{"title":"Extremal Results on Conflict-Free Coloring","authors":"Sriram Bhyravarapu, Shiwali Gupta, Subrahmanyam Kalyanasundaram, Rogers Mathew","doi":"10.1002/jgt.23223","DOIUrl":"https://doi.org/10.1002/jgt.23223","url":null,"abstract":"<div>\u0000 \u0000 A conflict-free open neighborhood (CFON) coloring of a graph is an assignment of colors to the vertices such that for every vertex there is a color that appears exactly once in its open neighborhood. For a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>, the smallest number of colors required for such a coloring is called the CFON chromatic number and is denoted by <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 \u0000 <mi>ON</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>. By considering closed neighborhood instead of open neighborhood, we obtain the analogous notions of conflict-free (CF) closed neighborhood (CFCN) coloring, and CFCN chromatic number (denoted by <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 \u0000 <mi>CN</mi>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>). The notion of CF coloring was introduced in 2002, and has since received considerable attention. We study CFON and CFCN colorings and show the following results. In what follows, <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> denotes the maximum degree of the graph.\u0000\u0000 <ul>\u0000 \u0000 <li>\u0000 We show that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 3","pages":"259-268"},"PeriodicalIF":0.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Polynomial Method for Three-Path Extendability of List Colourings of Planar Graphs 平面图表着色三路可拓的多项式方法

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-24 DOI: 10.1002/jgt.23214

Przemysław Gordinowicz, Paweł Twardowski

We restate Thomassen's theorem of 3-extendability (Thomassen, Journal of Combinatorial Theory Series B, 97, 571–583), an extension of the famous planar 5-choosability theorem, in terms of graph polynomials. This yields an Alon–Tarsi equivalent of 3-extendability.

我们用图多项式的形式重申了Thomassen的3-可扩展性定理（Thomassen, Journal of Combinatorial Theory Series B, 97, 571-583），这是著名的平面5-可选择性定理的推广。这产生了相当于3-可扩展性的Alon-Tarsi。

引用次数: 0

On the Multigraph Overfull Conjecture 关于多图过满猜想

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-09 DOI: 10.1002/jgt.23221

Michael J. Plantholt, Songling Shan

A subgraph $� � � � H � � �$ of a multigraph $� � � � G � � �$ is overfull if $� � � � ∣ � � E � � � (� � H � �) � � � ∣ � � > � � Δ � � � (� � G � �) � � � � ⌊ � � � ∣ � � V � � � (� � H � �) � � � ∣ � � / � � 2 � � � ⌋ � � � . � � �$ Analogous to the Overfull Conjecture proposed by Chetwynd and Hilton in 1986, Stiebitz et al. formed the multigraph version of the conjecture as follows: Let $� � � � G � � �$ be a multigraph with maximum multiplicity $� � � � r � � �$ and maximum degree $� � � �$

多图G的子图H如果∣E (H)是满的)∣&gt；Δ (g)⌊∣v (H)∣/ 2⌋。与Chetwynd和Hilton于1986年提出的Overfull猜想类似，Stiebitz等人形成了该猜想的多图版本如下：设G是一个多重图，具有最大多重性r和最大次Δ &gt；13r∣V (G)∣。那么G有色指数Δ (G)当且仅当G不包含过满子图。在本文中，我们证明了对于足够大且偶数n的多图过满猜想的以下三个结果：其中n =∣V (G)∣。 (1)若G为k正则且k≥r (N / 2 + 18)，那么G有一个1分解。这个结果也解决了第一作者和Tipnis从2001年开始的一个猜想，即在k的下界有一个常数误差。(2)若G包含过满子图且δ (G)≥r（n / 2 + 18），则χ ' (G) =≤0χ f ' (G)⌉ ,其中χ f ' (G)为？的分数色指数G . (3)若G的最小度至少为（1 + ε）) r n / 2对于任意0 &lt；ε & lt;1和G不包含过满子图，则χ ' (G) = Δ(g)。这个证明是基于多图分解成简单图的，我们证明了一个猜想的一个稍微弱一点的版本，这个猜想是由第一作者和Tipnis从1991年开始将多图分解成有约束的简单图。这一结果也引起了人们的独立兴趣。

{"title":"On the Multigraph Overfull Conjecture","authors":"Michael J. Plantholt, Songling Shan","doi":"10.1002/jgt.23221","DOIUrl":"https://doi.org/10.1002/jgt.23221","url":null,"abstract":"<div>\u0000 \u0000 A subgraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> of a multigraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> is overfull if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mi>Δ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mrow>\u0000 <mo>⌊</mo>\u0000 \u0000 <mrow>\u0000 <mo>∣</mo>\u0000 \u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mo>/</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>⌋</mo>\u0000 </mrow>\u0000 \u0000 <mo>.</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> Analogous to the Overfull Conjecture proposed by Chetwynd and Hilton in 1986, Stiebitz et al. formed the multigraph version of the conjecture as follows: Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> be a multigraph with maximum multiplicity <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math> and maximum degree <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"226-236"},"PeriodicalIF":0.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest 图分解为匹配线性森林和有界线性森林的复杂性

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-08 DOI: 10.1002/jgt.23208

Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier

<div> Deciding whether a graph can be edge-decomposed into a matching and a <math> <semantics> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <annotation> <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0001" wiley:location="equation/jgt23208-math-0001.png"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation> </semantics></math>-bounded linear forest was recently shown by Campbell, Hörsch, and Moore to be nonedeterministic Polynomial time (NP)-complete for every <math> <semantics> <mrow> <mrow> <mi>k</mi> <mo>≥</mo> <mn>9</mn> </mrow> </mrow> <annotation> <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0002" wiley:location="equation/jgt23208-math-0002.png"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>9</mn></mrow></mrow></math></annotation> </semantics></math>, and solvable in polynomial time for <math> <semantics> <mrow> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </mrow> <annotation> <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0003" wiley:location="equation/jgt23208-math-0003.png"><mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mrow></math></annotation> </semantics></math>. In the first part of this paper, we close this gap by showing that this problem is NP-complete for every <math> <semantics> <mrow> <mrow> <mi>k</mi> <mo>≥</mo> <mn>3</mn> </mrow> </mrow> <annotation> <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0004" wiley:location="equation/jgt23208-math-0004.png"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>3</mn>

确定图是否可以边分解为匹配和k<； math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0001" wiley:location="equation/jgt23208-math-0001.png"><mrow>< /mrow></mrow></ mrow></mrow></ mrow></mrow></ mrow></math>；-有界线性森林最近由Campbell， Hörsch，对于每k≥9，多项式时间（NP）是完全的<；math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0002”威利:位置= "方程/ jgt23208 -数学- 0002. png”祝辞& lt; mrow> & lt; mrow> & lt; mi> k< / mi> & lt; mo> unicode {x02265} & lt; / mo> & lt; mn> 9 & lt; / mn> & lt; / mrow> & lt; / mrow> & lt; / math>，且k = 1时在多项式时间内可解，2< math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208- jgt23208-math-0003.png"><mrow>< jgt23208- jgt23208-math-0003.png"><mrow>< jgt23208- jgt23208- jgt23208-math-0003.png"><mrow>< jgt23208- jgt23208- jgt23208- jgt23208-math-0003.png"><mrow>< /mrow>< mrow> =</ mrow>< m>1</ m>< m>,</ mrow><；。在本文的第一部分，我们通过证明这个问题对于每个k≥3是np完备的来缩小这个差距<；math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0004”威利:位置= "方程/ jgt23208 -数学- 0004. png”祝辞& lt; mrow> & lt; mrow> & lt; mi> k< / mi> & lt; mo> unicode {x02265} & lt; / mo> & lt; mn> 3 & lt; / mn> & lt; / mrow> & lt; / mrow> & lt; / math>。在论文的第二部分，我们证明了决定一个图是否可以边分解为一个匹配和一个k<； math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0005" wiley:location="equation/jgt23208-math-0005.png"><mrow><mrow>< /mrow></mrow></ mrow></mrow></ mrow></mrow></math>；-有界星林对任意k∈N∪{∞}多项式可解<math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23208:jgt23208- jgt23208-math-0006.png“><mrow><mrow>< mrow>< / mrow>< / mrow>< / mrow>< / mrow><mrow><mi mathvariant=”双划”>N</ m02208}</mo><mrow><mo class="MathClass-open">{</ mo0222a}</mo><mrow>< / mrow><类= " MathClass-close "祝辞}& lt; / mo> & lt; / mrow> & lt; / mrow> & lt; / mrow> & lt; / math>，回答Campbell、Hörsch和Moore在同一篇论文中提出的另一个问题。

{"title":"The Complexity of Decomposing a Graph into a Matching and a Bounded Linear Forest","authors":"Agnijo Banerjee, João Pedro Marciano, Adva Mond, Jan Petr, Julien Portier","doi":"10.1002/jgt.23208","DOIUrl":"https://doi.org/10.1002/jgt.23208","url":null,"abstract":"<div>\u0000 \u0000 Deciding whether a graph can be edge-decomposed into a matching and a <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0001\" wiley:location=\"equation/jgt23208-math-0001.png\"><mrow><mrow><mi>k</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>-bounded linear forest was recently shown by Campbell, Hörsch, and Moore to be nonedeterministic Polynomial time (NP)-complete for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>9</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0002\" wiley:location=\"equation/jgt23208-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>9</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>, and solvable in polynomial time for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0003\" wiley:location=\"equation/jgt23208-math-0003.png\"><mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. In the first part of this paper, we close this gap by showing that this problem is NP-complete for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23208:jgt23208-math-0004\" wiley:location=\"equation/jgt23208-math-0004.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>3</mn>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"76-87"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact Results for Generalized Extremal Problems Forbidding an Even Cycle 禁止偶环的广义极值问题的精确结果

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-08 DOI: 10.1002/jgt.23219

Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu

We determine the maximum number of copies of

�            � � �_{K �                  � � s �                     �, �                     � s � �} �

in a

�            � � �_{C �                  � � 2 �                     � s �                     � + �                     � 2 � �} �

-free

�            � � n �

-vertex graph for all integers

�            � � s �               � \geq �               � 2 �

and sufficiently large

�            � � n �

. Moreover, for

�            � � s �               � \in �               � � {�                  � � 2 �                     �, �                     � 3 � �                  �} � �

and any integer

�            � � n �

, we obtain the maximum number of cycles of length

�            � � 2 �               � s �

in an

�            � � n �

-vertex

�            � � �_{C �                  � � 2 �                     � s �                     � + �                     � 2 � �} �

-free bipartite graph.

我们确定K的最大拷贝数，对于所有整数，在一个c2s + 2自由的n顶点图中S≥2且n足够大。并且，对于s∈{2,3}和任意整数n，我们得到了n顶点c2s + 2自由中长度为2s的最大循环数由两部分构成的图。

{"title":"Exact Results for Generalized Extremal Problems Forbidding an Even Cycle","authors":"Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu","doi":"10.1002/jgt.23219","DOIUrl":"https://doi.org/10.1002/jgt.23219","url":null,"abstract":"<div>\u0000 \u0000 We determine the maximum number of copies of <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>s</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math> in a <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-free <math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-vertex graph for all integers <math>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow></math> and sufficiently large <math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>. Moreover, for <math>\u0000 \u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow></math> and any integer <math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>, we obtain the maximum number of cycles of length <math>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 </mrow></math> in an <math>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>-vertex <math>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>C</mi>\u0000 \u0000 <mrow>\u0000 <mn>2</mn>\u0000 \u0000 <mi>s</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-free bipartite graph.\u0000 </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"218-225"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143846094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Maximal Degrees in Subgraphs of Kneser Graphs Kneser图子图的极大度

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory

Pub Date : 2025-01-08 DOI: 10.1002/jgt.23213

Peter Frankl, Andrey Kupavskii

In this paper, we study the maximum degree in nonempty-induced subgraphs of the Kneser graph $� � � � � KG � � � (� � n � �, � � k � �) � � � � �$ . One of the main results asserts that, for $� � � � � k � � > � � �_{k � � 0 �} � � � �$ and $� � � � � n � � > � � 64 � � �^{k � � 2 �} � � � �$ , whenever a nonempty subgraph has

本文研究了Kneser图KG (n)的非空诱导子图的最大度。k) <math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0001”威利:位置= "方程/ jgt23213 -数学- 0001. png”祝辞& lt; mrow> & lt; mrow> & lt; mi> KG< / mi> & lt; mrow> & lt; mo> (& lt; / mo> & lt; mi&gt n< / mi> & lt; mo>, & lt; / mo> & lt; mi> k< / mi> & lt; mo>) & lt; / mo> & lt; / mrow> & lt; / mrow> & lt; / mrow> & lt; / math>。其中一个主要结果断言，对于k &gt；k 0< math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23213:jgt23213- jgt23213-math-0002" wiley:location="equation/jgt23213-math-0002.png"><mrow><mrow>< /jgt23213- jgt23213- jgt23213-math-0002.png"><mrow>< /jgt23213- jgt23213- jgt23213-math-0002.png"><mrow><mrow>< /msub>< msub>< msub></ msub></ msub></ msub></ msub></ msub></ msub></ msub></ msub></ msub></mrow></mrow></ mrow></math&gt；n &gt；64 k 2 <math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0003”威利:位置= "方程/ jgt23213 -数学- 0003. png”祝辞& lt; mrow> & lt; mrow> & lt; mi> n< / mi> & lt; mo> unicode {x0003E} & lt; / mo> & lt; mn> 64 & lt; / mn> & lt; msup> & lt; mi> k< / mi> & lt; mn> 2 & lt; / mn> & lt; / msup> & lt; / mrow> & lt; / mrow> & lt; / math>,当一个非空子图有m≥k n−2时k−2 <math xmlns="http://www.w3.org/1998/Math/MathML" altimg="urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0004" wiley:location=“equation/jgt23213-math-0004. ” png”祝辞& lt; mrow> & lt; mrow> & lt; mi> m< / mi> & lt; mo> unicode {x02265} & lt; / mo> & lt; mi> k< / mi> & lt; mfenced =”)“开放= "(“祝辞& lt; mfrac linethickness = " 0 "祝辞& lt; mrow> & lt; mi&gt n< / mi> & lt; mo> unicode {x02212} & lt; / mo> & lt; mn> 2 & lt; / mn> & lt; / mrow> & lt; mrow> & lt; mi> k< / mi> & lt; mo> unicode {x02212} & lt; / mo> & lt; mn> 2 & lt; / mn> & lt; / mrow> & lt; / mfrac> & lt; / mfenced> & lt; / mrow> & lt; / mrow> & lt; / math>顶点,它的最大度至少为1 2 1−k2

{"title":"Maximal Degrees in Subgraphs of Kneser Graphs","authors":"Peter Frankl, Andrey Kupavskii","doi":"10.1002/jgt.23213","DOIUrl":"https://doi.org/10.1002/jgt.23213","url":null,"abstract":"<div>\u0000 \u0000 In this paper, we study the maximum degree in nonempty-induced subgraphs of the Kneser graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>KG</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>k</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0001\" wiley:location=\"equation/jgt23213-math-0001.png\"><mrow><mrow><mi>KG</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math>. One of the main results asserts that, for <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <msub>\u0000 <mi>k</mi>\u0000 \u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0002\" wiley:location=\"equation/jgt23213-math-0002.png\"><mrow><mrow><mi>k</mi><mo>unicode{x0003E}</mo><msub><mi>k</mi><mn>0</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>64</mn>\u0000 \u0000 <msup>\u0000 <mi>k</mi>\u0000 \u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23213:jgt23213-math-0003\" wiley:location=\"equation/jgt23213-math-0003.png\"><mrow><mrow><mi>n</mi><mo>unicode{x0003E}</mo><mn>64</mn><msup><mi>k</mi><mn>2</mn></msup></mrow></mrow></math></annotation>\u0000 </semantics></math>, whenever a nonempty subgraph has <sp","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 1","pages":"88-96"},"PeriodicalIF":0.9,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143612439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

首页上一页

2
3
4
5
6
7
8
9
...
10

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Graph Theory

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀

0

微信

客服QQ

扫码关注我们

反馈

Book学术文献互助群
群号：604180095

文献互助智能选刊最新文献互助须知联系我们：info@booksci.cn

Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。

京公网安备 11010802042870号京ICP备2023020795号-1