Discrete Mathematics最新文献

英文中文

A spectral stability result regarding the complete bipartite graph K2,t 关于完全二部图K2，t的谱稳定性结果

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114914

Ruike Wang, Zhenzhen Lou

Spectral stability theorems have been a crucial aspect of graph theory research. Consider a graph G with size m and spectral radius

ρ (G)

. Building on the solid foundation laid by previous works in this rich field, this paper presents novel and valuable findings related to stability. Wang and Guo (2024) [16] showed an important result. Given that

m = Ω (k^{4})

and

k \geq 0

, when

ρ (G) \geq \sqrt{m - k}

, then G contains either a quadrilateral or a star of size

m - k

. In this paper, we take a significant step forward by generalizing this result. Precisely, for

m = Ω (k^{4})

and

2 \leq t \leq k + 2

, when

ρ (G) \geq \sqrt{m - k + t - 2}

, we prove that G contains either a copy of

K_{2, t}

(a complete bipartite graph with two vertices on one side and t vertices on the other side) or a star of size

m - k + t - 2

. This generalization contributes to a more profound understanding of the spectral and structural aspects of graphs, as well as their stability properties.

谱稳定性定理一直是图论研究的一个重要方面。考虑一个大小为m，谱半径为ρ(G)的图G。本文在前人在这一丰富领域的工作奠定的坚实基础上，提出了与稳定性有关的新颖而有价值的发现。Wang and Guo(2024)[16]给出了重要的结果。设m=Ω（k4）且k≥0，当ρ(G)≥m - k时，则G包含大小为m - k的四边形或星形。在本文中，我们通过推广这一结果向前迈出了重要的一步。准确地说，对于m=Ω（k4）和2≤t≤k+2，当ρ(G)≥m−k+t−2时，我们证明了G包含K2的一个副本，t（一侧有两个顶点，另一侧有t个顶点的完全二部图）或一个大小为m−k+t−2的星。这种推广有助于更深刻地理解图的谱和结构方面，以及它们的稳定性。

{"title":"A spectral stability result regarding the complete bipartite graph K2,t","authors":"Ruike Wang, Zhenzhen Lou","doi":"10.1016/j.disc.2025.114914","DOIUrl":"10.1016/j.disc.2025.114914","url":null,"abstract":"<div><div>Spectral stability theorems have been a crucial aspect of graph theory research. Consider a graph G with size m and spectral radius <math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math>. Building on the solid foundation laid by previous works in this rich field, this paper presents novel and valuable findings related to stability. Wang and Guo (2024) [16] showed an important result. Given that <math><mi>m</mi><mo>=</mo><mi>Ω</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math> and <math><mi>k</mi><mo>≥</mo><mn>0</mn></math>, when <math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><msqrt><mrow><mi>m</mi><mo>−</mo><mi>k</mi></mrow></msqrt></math>, then G contains either a quadrilateral or a star of size <math><mi>m</mi><mo>−</mo><mi>k</mi></math>. In this paper, we take a significant step forward by generalizing this result. Precisely, for <math><mi>m</mi><mo>=</mo><mi>Ω</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math> and <math><mn>2</mn><mo>≤</mo><mi>t</mi><mo>≤</mo><mi>k</mi><mo>+</mo><mn>2</mn></math>, when <math><mi>ρ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><msqrt><mrow><mi>m</mi><mo>−</mo><mi>k</mi><mo>+</mo><mi>t</mi><mo>−</mo><mn>2</mn></mrow></msqrt></math>, we prove that G contains either a copy of <math><msub><mrow><mi>K</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>t</mi></mrow></msub></math> (a complete bipartite graph with two vertices on one side and t vertices on the other side) or a star of size <math><mi>m</mi><mo>−</mo><mi>k</mi><mo>+</mo><mi>t</mi><mo>−</mo><mn>2</mn></math>. This generalization contributes to a more profound understanding of the spectral and structural aspects of graphs, as well as their stability properties.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 5","pages":"Article 114914"},"PeriodicalIF":0.7,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145697781","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

Corners of (t,tk ± 1)-core partitions （t,tk ± 1）-核分区的角

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114915

Hyunsoo Cho , Ho-Hyeong Lee , Kyeongjun Lee , Hayan Nam , Jaebum Sohn

Huang and Wang began counting the number of simultaneous core partitions with the fixed number of corners. They enumerated the number of

(t, t + 1)

-core partitions with m corners and

(t, t + 1, t + 2)

-core partitions with m corners. Later, Cho, Huh, and Sohn gave a formula for the number of

(t, t + 1, \dots, t + p)

-core partitions with m corners. In this paper, we show an expression for the number of

(t, t k \pm 1)

-core partitions with m corners.

黄和王开始计算同时具有固定角数的核心分区的数量。他们列举了有m个角的（t,t+1）核分区和有m个角的（t,t+1,t+2）核分区的数目。后来，Cho， Huh和Sohn给出了一个公式，表示有m个角的（t,t+1，…，t+p）核分区的数量。本文给出了具有m个角的（t,tk±1）个核分区数目的表达式。

引用次数: 0

Ramsey goodness of large books revisited 拉姆齐善良的大部头书重访

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114937

Meng Liu , Yusheng Li

For a graph G, a connected graph H is said to be G-good if the Ramsey number

r (G, H)

is equal to the lower bound

(χ (G) - 1) (| H | - 1) + s (G)

, where

χ (G)

and

s (G)

are the chromatic number and the chromatic surplus of G, respectively. Let

B_{k} (n)

be the book graph that consists of n copies of

K_{k + 1}

sharing a common

K_{k}

. Recently, avoiding use of the regularity lemma, Fox, He and Wigderson (2023) revisit several Ramsey goodness results involving books. They commented that it would be very interesting to see how far one can push these ideas. In this paper, we describe graphs G with

s (G) = 1

exactly such that

B_{k} (n)

are G-good for large n, where the size of a color class of G can be at most δn for some

δ > 0

对于图G，如果Ramsey数r（G，H）等于下界（χ(G)−1）(|H|−1)+s(G)，则连通图H是G-good，其中χ(G)和s(G)分别是G的色数和色余。设Bk(n)是由n个Kk+1的副本组成的书图，它有一个共同的Kk。最近，为了避免使用规律性引理，Fox， He和Wigderson（2023）重新审视了几个涉及书籍的拉姆齐良数结果。他们评论说，看看一个人能把这些想法推进多远，这将是非常有趣的。在本文中，我们描述了s(G)=1的图G，使得Bk(n)在n大的情况下是G-good的，其中对于某些δ>；0， G的颜色类的大小最多可以是δn。

{"title":"Ramsey goodness of large books revisited","authors":"Meng Liu , Yusheng Li","doi":"10.1016/j.disc.2025.114937","DOIUrl":"10.1016/j.disc.2025.114937","url":null,"abstract":"<div><div>For a graph G, a connected graph H is said to be G-good if the Ramsey number <math><mi>r</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>H</mi><mo>)</mo></math> is equal to the lower bound <math><mo>(</mo><mi>χ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mo>|</mo><mi>H</mi><mo>|</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>s</mi><mo>(</mo><mi>G</mi><mo>)</mo></math>, where <math><mi>χ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math> and <math><mi>s</mi><mo>(</mo><mi>G</mi><mo>)</mo></math> are the chromatic number and the chromatic surplus of G, respectively. Let <math><msub><mrow><mi>B</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math> be the book graph that consists of n copies of <math><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math> sharing a common <math><msub><mrow><mi>K</mi></mrow><mrow><mi>k</mi></mrow></msub></math>. Recently, avoiding use of the regularity lemma, Fox, He and Wigderson (2023) revisit several Ramsey goodness results involving books. They commented that it would be very interesting to see how far one can push these ideas. In this paper, we describe graphs G with <math><mi>s</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mn>1</mn></math> exactly such that <math><msub><mrow><mi>B</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math> are G-good for large n, where the size of a color class of G can be at most δn for some <math><mi>δ</mi><mo>></mo><mn>0</mn></math>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 5","pages":"Article 114937"},"PeriodicalIF":0.7,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145697837","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

A note on 2-quasi-bisection of cubic graphs with oddness 2 奇数为2的三次图的2-拟对分的一个注记

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114939

Siyan Liu , Rong-Xia Hao , Rong Luo , Cun-Quan Zhang

A k-bisection (resp. k-quasi-bisection) of a bridgeless cubic graph G is a vertex 2-coloring satisfying: (i) the sizes of the two color classes are equal (resp. the sizes of the two color classes differ by at most 2), and (ii) the order of each connected component induced by each color class is at most k. Esperet et al. (2017) [7] conjectured that any cubic graph admits a 2-quasi-bisection. In this paper, we prove this conjecture for all bridgeless cubic graphs with oddness 2.

k-二分法。无桥三次图G的k-拟对分（k-拟对分）是顶点2着色，满足：(i)两个颜色类的大小相等(相对于；两个颜色类的大小相差不超过2)，并且（ii）每个颜色类诱导的每个连通分量的阶数不超过k。Esperet et al.(2017)[7]推测任何三次图都允许2-拟对分。本文对奇异数为2的所有无桥三次图证明了这一猜想。

引用次数: 0

Lower bounds for book Ramsey numbers 书本拉姆齐数的下界

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114913

William J. Wesley

We prove new bounds for Ramsey numbers for book graphs

B_{n}

. In particular, we show that

R (B_{n - 1}, B_{n}) = 4 n - 1

for an infinite family of n using a block-circulant construction similar to Paley graphs. We obtain improved bounds for several other values of

R (B_{r}, B_{s})

using different block-circulant graphs from SAT and integer programming (IP) solvers. Finally, we enumerate the number of critical graphs for

R (B_{r}, B_{s})

for small r and s using SAT modulo symmetries (SMS).

我们证明了书本图Bn的拉姆齐数的新界。特别地，我们用类似于Paley图的块循环构造证明了对于无限族n， R(Bn−1,Bn)=4n−1。我们利用SAT和整数规划（IP）求解器中的不同块循环图，得到了R（Br, b）的其他几个值的改进界。最后，我们用SAT模对称（SMS）列举了R（Br,Bs）对于小R和s的临界图的数目。

引用次数: 0

Bilateral truncated quintuple product identity 双边截断五元积恒等式

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114916

Wenxia Qu , Wenston J.T. Zang

In this paper, we present the bilateral truncated identity of the quintuple product identity, which is a generalization of the truncated quintuple product identities given by Chan et al. (2016) [6]. Additionally, we provide the bilateral truncated forms of two q-series identities, which are well-known consequences of the quintuple product identity.

在本文中，我们提出了五元组乘积恒等式的双边截断恒等式，它是Chan等人（2016）[6]给出的截断五元组乘积恒等式的推广。此外，我们提供了两个q级数恒等式的双边截断形式，这是众所周知的五元积恒等式的结果。

引用次数: 0

A new class of self-orthogonal linear codes and their applications 一类新的自正交线性码及其应用

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-08 DOI: 10.1016/j.disc.2025.114935

Yaozong Zhang, Dabin Zheng, Xiaoqiang Wang

Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received continuous attention and research. In this paper, we construct a class of self-orthogonal codes by using the defining-set approach, and determine their weight distributions and the parameters of their dual codes. Some considered codes are optimal according to the tables of best codes known maintained at [11] and a class of almost maximum distance separable (AMDS) codes from their duals is obtained. As applications, we obtain a class of new quantum codes, which are MDS or AMDS according to the quantum Singleton bound under certain conditions. Some examples show that the constructed quantum codes have the better parameters than known ones maintained at [6]. Furthermore, a new class of LCD codes is given, which are almost optimal according to the sphere packing bound.

自正交码是包含在对偶码内的线性码的一个子类。由于自正交码在量子码、晶格理论和线性互补对偶（LCD）码中得到了广泛的应用，一直受到人们的关注和研究。本文利用定义集方法构造了一类自正交码，并确定了它们的权值分布及其对偶码的参数。根据已知最优码表在[11]处保持的最佳码，得到了一类与其对偶的几乎最大距离可分离码（AMDS）。作为应用，我们在一定条件下根据量子单态界得到了一类新的量子码，即MDS或AMDS。一些实例表明，所构建的量子码在[6]下具有比已知量子码更好的参数。在此基础上，给出了一类新的LCD编码，它几乎是最优的。

引用次数: 0

On nonsingular weightwise perfectly balanced functions 在非奇异权完全平衡函数上

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-05 DOI: 10.1016/j.disc.2025.114919

Xinyi Zhao , Shizhu Tian , Xiangyong Zeng , Zhimin Sun

Boolean functions restricted to some subset of

F_{2}^{n}

play an important role in the FLIP stream cipher proposed by Méaux et al. in 2016. Carlet et al. later studied the particular case where the subset is composed of vectors with constant Hamming weight, known as weightwise perfectly balanced (WPB) functions. Motivated by the application of nonsingular functions in stream ciphers based on feedback shift registers (FSRs), in this paper, we focus on nonsingular WPB functions. Firstly, we propose an algorithm based on the truth tables to generate all nonsingular WPB functions. A concrete construction of such functions is also provided. Considering the security in different application scenarios, we further investigate their nonlinearity and cycle structure. A tight lower bound on the nonlinearity is obtained, as well as a theoretical probability distribution of the nonlinearity. Notably, our lower bound is higher than the known lower bound on WPB functions. To generate nonsingular WPB functions with high nonlinearity, an improved algorithm is also proposed. Finally, we offer a method to analyze the cycle structure of nonsingular WPB functions, and a method to obtain such functions which generate a few cycles. Experiments show that nonsingular WPB functions are suitable for constructing de Bruijn sequences with cycle-joining method.

限制于F2n的某个子集的布尔函数在msamuaux等人于2016年提出的FLIP流密码中发挥了重要作用。Carlet等人后来研究了一种特殊情况，其中子集由具有恒定汉明权重的向量组成，称为加权完美平衡（WPB）函数。基于非奇异函数在基于反馈移位寄存器（FSRs）的流密码中的应用，本文重点研究了非奇异WPB函数。首先，我们提出了一种基于真值表的非奇异WPB函数生成算法。还提供了这些函数的具体结构。考虑到不同应用场景下的安全性，我们进一步研究了它们的非线性和周期结构。得到了非线性的一个紧下界，以及非线性的理论概率分布。值得注意的是，我们的下界高于已知的WPB函数的下界。为了生成高度非线性的非奇异WPB函数，提出了一种改进算法。最后，我们给出了一种分析非奇异WPB函数的环结构的方法，以及一种获取产生少量环的非奇异WPB函数的方法。实验表明，非奇异WPB函数适用于用循环连接法构造de Bruijn序列。

{"title":"On nonsingular weightwise perfectly balanced functions","authors":"Xinyi Zhao , Shizhu Tian , Xiangyong Zeng , Zhimin Sun","doi":"10.1016/j.disc.2025.114919","DOIUrl":"10.1016/j.disc.2025.114919","url":null,"abstract":"<div><div>Boolean functions restricted to some subset of <math><msubsup><mrow><mi>F</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math> play an important role in the FLIP stream cipher proposed by Méaux et al. in 2016. Carlet et al. later studied the particular case where the subset is composed of vectors with constant Hamming weight, known as weightwise perfectly balanced (WPB) functions. Motivated by the application of nonsingular functions in stream ciphers based on feedback shift registers (FSRs), in this paper, we focus on nonsingular WPB functions. Firstly, we propose an algorithm based on the truth tables to generate all nonsingular WPB functions. A concrete construction of such functions is also provided. Considering the security in different application scenarios, we further investigate their nonlinearity and cycle structure. A tight lower bound on the nonlinearity is obtained, as well as a theoretical probability distribution of the nonlinearity. Notably, our lower bound is higher than the known lower bound on WPB functions. To generate nonsingular WPB functions with high nonlinearity, an improved algorithm is also proposed. Finally, we offer a method to analyze the cycle structure of nonsingular WPB functions, and a method to obtain such functions which generate a few cycles. Experiments show that nonsingular WPB functions are suitable for constructing de Bruijn sequences with cycle-joining method.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 4","pages":"Article 114919"},"PeriodicalIF":0.7,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693656","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

Paired domination in graphs with minimum degree four 最小次为4的图中的成对支配

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-05 DOI: 10.1016/j.disc.2025.114923

Csilla Bujtás , Michael A. Henning

A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S admits a perfect matching. The minimum cardinality of a paired dominating set of G is the paired domination number

γ_{pr} (G)

of G. We show that if G is a graph of order n and

δ (G) \geq 4

, then

γ_{pr} (G) \leq \frac{10}{17} n < 0.5883 n

如果图G中的每个顶点都与S中的一个顶点相邻，且由S引生的子图完全匹配，则图G中的顶点集S就是配对支配集。G的配对支配集的最小基数是G的配对支配数γpr(G)。我们证明了如果G是n阶图且δ(G)≥4，则γpr(G)≤1017n<0.5883n。

引用次数: 0

Sufficient conditions for edge-colored bipartite graphs to have rainbow and properly colored spanning trees 边色二部图具有彩虹和适当着色生成树的充分条件

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-12-04 DOI: 10.1016/j.disc.2025.114921

Shinya Fujita , Mikio Kano , Shun-ichi Maezawa , Masao Tsugaki , Kiyoshi Yoshimoto

An edge-colored graph is called rainbow if no two edges have the same color. An edge-colored graph is called properly colored if no two adjacent edges have the same color. We consider a connected edge-colored bipartite graph

G = G (A, B)

with bipartition

(A, B)

in which for every color c, the set of edges colored with c forms a star. It is known that if the minimum color degree of G is at least

| G | / 3 + 1

, then G has a rainbow spanning tree. In this paper, we prove that if the minimum color degree of G is at least

(\max {| A |, | B |} + 2) / 2

, then G has a rainbow spanning tree. Our theorem strengthens the previous result. We also provide a similar sufficient condition for connected edge-colored bipartite graphs to have properly colored spanning trees. Moreover, we show that these minimum color degree conditions are sharp.

如果没有两条边的颜色相同，则称为彩虹。如果没有两条相邻的边具有相同的颜色，则称为正确着色的图。我们考虑一个具有二分（a，B）的连通边着色二部图G=G(a，B)，其中对于每一种颜色c，用c着色的边的集合形成一个星形。已知，如果G的最小色度至少为|G|/3+1，则G具有彩虹生成树。在本文中，我们证明了如果G的最小色度至少为(max {|A|,|B|}+2)/2，则G存在彩虹生成树。我们的定理加强了前面的结果。我们也给出了连通边着色二部图具有适当着色生成树的一个类似的充分条件。此外，我们表明这些最小色度条件是清晰的。

{"title":"Sufficient conditions for edge-colored bipartite graphs to have rainbow and properly colored spanning trees","authors":"Shinya Fujita , Mikio Kano , Shun-ichi Maezawa , Masao Tsugaki , Kiyoshi Yoshimoto","doi":"10.1016/j.disc.2025.114921","DOIUrl":"10.1016/j.disc.2025.114921","url":null,"abstract":"<div><div>An edge-colored graph is called rainbow if no two edges have the same color. An edge-colored graph is called properly colored if no two adjacent edges have the same color. We consider a connected edge-colored bipartite graph <math><mi>G</mi><mo>=</mo><mi>G</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> with bipartition <math><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> in which for every color c, the set of edges colored with c forms a star. It is known that if the minimum color degree of G is at least <math><mo>|</mo><mi>G</mi><mo>|</mo><mo>/</mo><mn>3</mn><mo>+</mo><mn>1</mn></math>, then G has a rainbow spanning tree. In this paper, we prove that if the minimum color degree of G is at least <math><mrow><mo>(</mo><mi>max</mi><mo>⁡</mo><mo>{</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>B</mi><mo>|</mo><mo>}</mo><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mo>/</mo><mn>2</mn></math>, then G has a rainbow spanning tree. Our theorem strengthens the previous result. We also provide a similar sufficient condition for connected edge-colored bipartite graphs to have properly colored spanning trees. Moreover, we show that these minimum color degree conditions are sharp.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 4","pages":"Article 114921"},"PeriodicalIF":0.7,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693655","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

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

Discrete Mathematics

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.

﹀