Journal of Combinatorial Theory Series B最新文献

英文中文

Reconfiguration of basis pairs in regular matroids 正则拟阵中基对的重构

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-03-01 Epub Date: 2025-11-14 DOI: 10.1016/j.jctb.2025.10.009

Kristóf Bérczi , Bence Mátravölgyi , Tamás Schwarcz

In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns the exchange distance of two matroid basis sequences, a problem that appears in several areas of computer science and mathematics. White (1980) proposed a conjecture for the characterization of two basis sequences being reachable from each other by symmetric exchanges, which received a significant interest also in algebra due to its connection to toric ideals and Gröbner bases. In this work, we verify White's conjecture for basis sequences of length two in regular matroids, a problem that was formulated as a separate question by Farber, Richter, and Shank (1985) and Andres, Hochstättler, and Merkel (2014). Most of previous work on White's conjecture has not considered the question from an algorithmic perspective. We study the problem from an optimization point of view: our proof implies a polynomial algorithm for determining a sequence of symmetric exchanges that transforms a basis pair into another, thus providing the first polynomial upper bound on the exchange distance of basis pairs in regular matroids. As a byproduct, we verify a conjecture of Gabow (1976) on the serial symmetric exchange property of matroids for the regular case.

近年来，组合重构问题由于与优化、计数、枚举或抽样等各种主题的联系而引起了人们的广泛关注。最有趣的开放问题之一涉及两个矩阵基序列的交换距离，这个问题出现在计算机科学和数学的几个领域。White（1980）提出了一个关于两个基序列通过对称交换可相互到达的表征的猜想，由于它与环态理想和Gröbner基的联系，该猜想在代数中也引起了极大的兴趣。在这项工作中，我们验证了White关于正则拟阵中长度为2的基序列的猜想，这个问题被Farber， Richter, and Shank (1985), Andres, Hochstättler, and Merkel（2014）作为一个单独的问题公式化。怀特猜想之前的大部分工作都没有从算法的角度考虑这个问题。我们从最优化的角度研究了这个问题：我们的证明包含了一个多项式算法，用于确定将一个基对转化为另一个基对的对称交换序列，从而提供了正则拟阵中基对交换距离的第一个多项式上界。作为一个副产品，我们在正则情况下验证了Gabow（1976）关于拟阵的序列对称交换性质的一个猜想。

{"title":"Reconfiguration of basis pairs in regular matroids","authors":"Kristóf Bérczi , Bence Mátravölgyi , Tamás Schwarcz","doi":"10.1016/j.jctb.2025.10.009","DOIUrl":"10.1016/j.jctb.2025.10.009","url":null,"abstract":"<div><div>In recent years, combinatorial reconfiguration problems have attracted great attention due to their connection to various topics such as optimization, counting, enumeration, or sampling. One of the most intriguing open questions concerns the exchange distance of two matroid basis sequences, a problem that appears in several areas of computer science and mathematics. White (1980) proposed a conjecture for the characterization of two basis sequences being reachable from each other by symmetric exchanges, which received a significant interest also in algebra due to its connection to toric ideals and Gröbner bases. In this work, we verify White's conjecture for basis sequences of length two in regular matroids, a problem that was formulated as a separate question by Farber, Richter, and Shank (1985) and Andres, Hochstättler, and Merkel (2014). Most of previous work on White's conjecture has not considered the question from an algorithmic perspective. We study the problem from an optimization point of view: our proof implies a polynomial algorithm for determining a sequence of symmetric exchanges that transforms a basis pair into another, thus providing the first polynomial upper bound on the exchange distance of basis pairs in regular matroids. As a byproduct, we verify a conjecture of Gabow (1976) on the serial symmetric exchange property of matroids for the regular case.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"177 ","pages":"Pages 105-142"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Non-linear Hamilton cycles in linear quasirandom and uniformly dense hypergraphs 线性准随机和均匀稠密超图中的非线性Hamilton环

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-03-01 Epub Date: 2025-11-05 DOI: 10.1016/j.jctb.2025.10.006

Jie Han , Xichao Shu , Guanghui Wang

A k-graph H is called

(p, μ)

-dense if for all not necessarily distinct sets

A_{1}, \dots, A_{k} \subseteq V (H)

we have

e (A_{1}, \dots, A_{k}) \geq p | A_{1} | \dots | A_{k} | - μ | V (H) |^{k}

. This is believed to be the weakest form of quasirandomness in k-graphs and also known as linear quasirandomness.

In this paper, we show that for

ℓ < k

satisfying

(k - ℓ) ∤ k

(p, μ)

-density plus a minimum

(ℓ + 1)

-degree of

α n^{k - ℓ - 1}

guarantees Hamilton ℓ-cycles, but requiring a minimum ℓ-degree of

Ω (n^{k - ℓ})

instead is not sufficient. This answers a question of Lenz–Mubayi–Mycroft and characterizes the triples

(k, ℓ, d)

when

k - ℓ ∤ k

such that degenerate choices of p and α force ℓ-Hamiltonicity.

We actually prove a general result on ℓ-Hamiltonicity in quasirandom k-graphs, assuming a minimum vertex degree and essentially that every two ℓ-sets can be connected by a constant length ℓ-path. This reduces the ℓ-Hamiltonicity problem to the study of the connection property which also allows us to deduce a

(k / 2)

-Hamiltonicity result in uniformly dense k-graphs (for even

k \geq 4

Our proof uses the lattice-based absorption method in the non-standard way and is the first one that embeds a non-linear Hamilton cycle in linear quasirandom k-graphs.

如果对于所有不一定不同的集合A1，…，Ak，我们有e(A1，…，Ak)≥p|A1|⋯|Ak|−μ|V(H)|k，则称k图H为（p,μ）密集。这被认为是k图中最弱的拟随机形式，也被称为线性拟随机。在本文中，我们证明了对于满足(k−r)∤k, (p,μ)-密度加上αnk−r - 1的最小(r +1)-度保证了Hamilton r -环，但要求最小r -度为Ω（k−r）是不够的。这回答了Lenz-Mubayi-Mycroft的一个问题，并描述了当k−r∤k时三元组（k, r,d）使得p和α力的选择退化为r -哈密顿性。我们实际上证明了一个关于准随机k图中r -哈密性的一般结果，假设有一个最小顶点度，并且本质上每两个r -集合都可以通过一个常数长度的r -路径连接起来。这就将l -哈密性问题简化为对连接性质的研究，这也使我们能够在均匀密集的k图中推导出(k/2)-哈密性结果（即使k≥4）。我们的证明以非标准的方式使用基于格的吸收方法，并且是第一个在线性准随机k图中嵌入非线性汉密尔顿循环的证明。

引用次数: 0

When recursion is better than iteration: A linear-time algorithm for directed acyclicity with few error vertices 当递归优于迭代时：一种具有少量错误顶点的有向非循环线性时间算法

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-03-01 Epub Date: 2025-11-17 DOI: 10.1016/j.jctb.2025.11.002

Daniel Lokshtanov , M.S. Ramanujan , Saket Saurabh

Planarity, bipartiteness and (directed) acyclicity are basic graph properties with classic linear-time recognition algorithms. However, the problems of testing whether a given graph has k vertices whose deletion makes it planar, bipartite or a directed acyclic graph (DAG) are all fundamental NP-complete problems when k is part of the input. As a result, a significant amount of research has been devoted to understanding whether, for every fixed k, these problems admit a polynomial-time algorithm (where the exponent in the polynomial is independent of k) and in particular, whether they admit linear-time algorithms.

While we now know that for every fixed k, we can test in linear time whether a graph is k vertices away from being planar or bipartite, the best known algorithms in the case of directed acyclicity are the algorithm of Garey and Tarjan [IPL 1978], which runs in time

O (n^{k - 1} \cdot m)

and the algorithm of Chen, Liu, Lu, O'Sullivan and Razgon [JACM 2008], which runs in time

O (k! \cdot 4^{k} \cdot k^{4} \cdot n \cdot m)

, where n and m are the number of vertices and arcs in the input digraph, respectively. In other words, it has remained open whether it is possible to recognize in linear time, a graph that is two vertices away from being acyclic.

In this paper, we settle this question by giving an algorithm that decides whether a given graph is k vertices away from being acyclic, in time

O (k! \cdot 4^{k} \cdot k^{5} \cdot (n + m))

. That is, for every fixed k, our algorithm runs in time

O (m + n)

, thus mirroring the case for planarity and bipartiteness.

We obtain our algorithm by introducing a general methodology that shaves off a factor of n from certain algorithms that use the powerful technique of iterative compression. The two main features of our methodology are: (i) This is the first generic technique for designing linear-time FPT algorithms for directed cut problems and (ii) it can be used in combination with future improvements in algorithms for the so-called compression version of other well-studied cut problems such as Multicut and Directed Subset Feedback Vertex Set.

平面性、二分性和（有向）非环性是经典线性时间识别算法的基本图性。然而，当k是输入的一部分时，检验给定图是否有k个顶点的缺失使其成为平面、二部或有向无环图（DAG）的问题都是基本的np完全问题。因此，大量的研究致力于理解，对于每个固定的k，这些问题是否允许多项式时间算法（其中多项式中的指数与k无关），特别是，它们是否允许线性时间算法。

{"title":"When recursion is better than iteration: A linear-time algorithm for directed acyclicity with few error vertices","authors":"Daniel Lokshtanov , M.S. Ramanujan , Saket Saurabh","doi":"10.1016/j.jctb.2025.11.002","DOIUrl":"10.1016/j.jctb.2025.11.002","url":null,"abstract":"<div><div>Planarity, bipartiteness and (directed) acyclicity are basic graph properties with classic linear-time recognition algorithms. However, the problems of testing whether a given graph has k vertices whose deletion makes it planar, bipartite or a directed acyclic graph (DAG) are all fundamental NP-complete problems when k is part of the input. As a result, a significant amount of research has been devoted to understanding whether, for every fixed k, these problems admit a polynomial-time algorithm (where the exponent in the polynomial is independent of k) and in particular, whether they admit linear-time algorithms.</div><div>While we now know that for every fixed k, we can test in linear time whether a graph is k vertices away from being planar or bipartite, the best known algorithms in the case of directed acyclicity are the algorithm of Garey and Tarjan [IPL 1978], which runs in time <math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>⋅</mo><mi>m</mi><mo>)</mo></math> and the algorithm of Chen, Liu, Lu, O'Sullivan and Razgon [JACM 2008], which runs in time <math><mi>O</mi><mo>(</mo><mi>k</mi><mo>!</mo><mo>⋅</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>⋅</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>⋅</mo><mi>n</mi><mo>⋅</mo><mi>m</mi><mo>)</mo></math>, where n and m are the number of vertices and arcs in the input digraph, respectively. In other words, it has remained open whether it is possible to recognize in linear time, a graph that is two vertices away from being acyclic.</div><div>In this paper, we settle this question by giving an algorithm that decides whether a given graph is k vertices away from being acyclic, in time <math><mi>O</mi><mo>(</mo><mi>k</mi><mo>!</mo><mo>⋅</mo><msup><mrow><mn>4</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>⋅</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>5</mn></mrow></msup><mo>⋅</mo><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>)</mo><mo>)</mo></math>. That is, for every fixed k, our algorithm runs in time <math><mi>O</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>n</mi><mo>)</mo></math>, thus mirroring the case for planarity and bipartiteness.</div><div>We obtain our algorithm by introducing a general methodology that shaves off a factor of n from certain algorithms that use the powerful technique of iterative compression. The two main features of our methodology are: (i) This is the first generic technique for designing linear-time FPT algorithms for directed cut problems and (ii) it can be used in combination with future improvements in algorithms for the so-called compression version of other well-studied cut problems such as Multicut and Directed Subset Feedback Vertex Set.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"177 ","pages":"Pages 143-185"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Extremal density for subdivisions with length or sparsity constraints 具有长度或稀疏性约束的细分的极值密度

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-03-01 Epub Date: 2025-11-17 DOI: 10.1016/j.jctb.2025.11.001

Jaehoon Kim , Hong Liu , Yantao Tang , Guanghui Wang , Donglei Yang , Fan Yang

Given a graph H, a balanced subdivision of H is obtained by replacing all edges of H with internally disjoint paths of the same length. In this paper, we prove that for any graph H, a linear-in-

e (H)

bound on average degree guarantees a balanced H-subdivision. This strengthens an old result of Bollobás and Thomason, and resolves a question of Gil-Fernández, Hyde, Liu, Pikhurko and Wu.

We observe that this linear bound on average degree is best possible whenever H is logarithmically dense. We further show that this logarithmic density is the critical threshold: for many graphs H below this density, its subdivisions are forcible by a sublinear-in-

e (H)

bound on average degree. We provide such examples by proving that the subdivisions of any almost bipartite graph H with sublogarithmic density are forcible by a sublinear-in-

e (H)

bound on average degree, provided that H satisfies some additional separability condition.

给定图H，通过将H的所有边替换为相同长度的内部不相交路径，得到H的均衡细分。本文证明了对于任意图H，在平均度上的线性- In -e(H)界保证了均衡的H细分。这加强了Bollobás和Thomason的一个老结果，解决了Gil-Fernández、Hyde、Liu、Pikhurko和Wu的问题。

{"title":"Extremal density for subdivisions with length or sparsity constraints","authors":"Jaehoon Kim , Hong Liu , Yantao Tang , Guanghui Wang , Donglei Yang , Fan Yang","doi":"10.1016/j.jctb.2025.11.001","DOIUrl":"10.1016/j.jctb.2025.11.001","url":null,"abstract":"<div><div>Given a graph H, a balanced subdivision of H is obtained by replacing all edges of H with internally disjoint paths of the same length. In this paper, we prove that for any graph H, a linear-in-<math><mi>e</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> bound on average degree guarantees a balanced H-subdivision. This strengthens an old result of Bollobás and Thomason, and resolves a question of Gil-Fernández, Hyde, Liu, Pikhurko and Wu.</div><div>We observe that this linear bound on average degree is best possible whenever H is logarithmically dense. We further show that this logarithmic density is the critical threshold: for many graphs H below this density, its subdivisions are forcible by a sublinear-in-<math><mi>e</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> bound on average degree. We provide such examples by proving that the subdivisions of any almost bipartite graph H with sublogarithmic density are forcible by a sublinear-in-<math><mi>e</mi><mo>(</mo><mi>H</mi><mo>)</mo></math> bound on average degree, provided that H satisfies some additional separability condition.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"177 ","pages":"Pages 67-104"},"PeriodicalIF":1.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Reuniting χ-boundedness with polynomial χ-boundedness 将χ-有界性与多项式χ-有界性重新统一

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-08-28 DOI: 10.1016/j.jctb.2025.08.002

Maria Chudnovsky , Linda Cook , James Davies , Sang-il Oum

A class

F

of graphs is χ-bounded if there is a function f such that

χ (H) \leq f (ω (H))

for all induced subgraphs H of a graph in

F

. If f can be chosen to be a polynomial, we say that

F

is polynomially χ-bounded. Esperet proposed a conjecture that every χ-bounded class of graphs is polynomially χ-bounded. This conjecture has been disproved; it has been shown that there are classes of graphs that are χ-bounded but not polynomially χ-bounded. Nevertheless, inspired by Esperet's conjecture, we introduce Pollyanna classes of graphs. A class

C

of graphs is Pollyanna if

C \cap F

is polynomially χ-bounded for every χ-bounded class

F

of graphs. We prove that several classes of graphs are Pollyanna and also present some proper classes of graphs that are not Pollyanna.

如果存在一个函数F，使得F中图的所有诱导子图H的χ(H)≤F (ω(H))，则一类图F是χ-有界的。如果F可以选择为多项式，则我们说F是多项式χ-有界的。Esperet提出了一个猜想，即每一类有χ有界的图都是多项式有χ有界的。这个猜想已经被推翻了；已经证明有一类图是χ有界的，但不是多项式χ有界的。然而，受Esperet猜想的启发，我们引入了波利安娜图类。如果C∩F对于每一个有χ有界的图类F都是多项式χ有界的，那么C类图就是波利安娜。我们证明了几类图是盲目乐观的，并给出了一些非盲目乐观图的适当类别。

{"title":"Reuniting χ-boundedness with polynomial χ-boundedness","authors":"Maria Chudnovsky , Linda Cook , James Davies , Sang-il Oum","doi":"10.1016/j.jctb.2025.08.002","DOIUrl":"10.1016/j.jctb.2025.08.002","url":null,"abstract":"<div><div>A class <math><mi>F</mi></math> of graphs is χ-bounded if there is a function f such that <math><mi>χ</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>≤</mo><mi>f</mi><mo>(</mo><mi>ω</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>)</mo></math> for all induced subgraphs H of a graph in <math><mi>F</mi></math>. If f can be chosen to be a polynomial, we say that <math><mi>F</mi></math> is polynomially χ-bounded. Esperet proposed a conjecture that every χ-bounded class of graphs is polynomially χ-bounded. This conjecture has been disproved; it has been shown that there are classes of graphs that are χ-bounded but not polynomially χ-bounded. Nevertheless, inspired by Esperet's conjecture, we introduce Pollyanna classes of graphs. A class <math><mi>C</mi></math> of graphs is Pollyanna if <math><mi>C</mi><mo>∩</mo><mi>F</mi></math> is polynomially χ-bounded for every χ-bounded class <math><mi>F</mi></math> of graphs. We prove that several classes of graphs are Pollyanna and also present some proper classes of graphs that are not Pollyanna.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"176 ","pages":"Pages 30-73"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144907692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Splitting-off in hypergraphs 超图中的分裂

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-10-09 DOI: 10.1016/j.jctb.2025.09.004

Kristóf Bérczi , Karthekeyan Chandrasekaran , Tamás Király , Shubhang Kulkarni

The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lovász [47], [49] and Mader [50] showed the existence of this operation while preserving global and local connectivities respectively in graphs under certain conditions. These results have far-reaching applications in graph algorithms literature [3], [9], [10], [14], [19], [24], [25], [26], [27], [28], [31], [32], [34], [35], [37], [40], [42], [43], [48], [50], [51], [52], [53]. In this work, we introduce a splitting-off operation in hypergraphs. We show that there exists a local connectivity preserving complete splitting-off in hypergraphs and give a strongly polynomial-time algorithm to compute it in weighted hypergraphs. We illustrate the usefulness of our splitting-off operation in hypergraphs by showing two applications: (1) we give a constructive characterization of k-hyperedge-connected hypergraphs and (2) we give an alternate proof of an approximate min-max relation for max Steiner rooted-connected orientation of graphs and hypergraphs (due to Király and Lau (2008) [40]). Our proof of the approximate min-max relation for graphs circumvents the Nash-Williams' strong orientation theorem and uses tools developed for hypergraphs.

无向图的分离操作是一种基本的约简操作，它将与给定顶点相关的所有边分离，并在该顶点的相邻边之间添加新边，同时保留其度数。Lovász[47]，[49]和Mader[50]分别证明了在一定条件下保持图的全局连通性和局部连通性的情况下，该操作的存在性。这些结果有影响深远的应用图算法文献[3],[9],[10],[14],[19],[24],[25],[26],[27],[28],[31],[32],[34],[35],[37],[40],[42],[43],[48],[50],[51],[52],[53]。在这项工作中，我们在超图中引入了一个分离操作。我们证明了超图中存在一个局部连通性保持完全分离，并给出了一个在加权超图中计算它的强多项式时间算法。我们通过展示两个应用来说明我们的分离操作在超图中的有用性：(1)我们给出了k-超边连接超图的建设性表征；(2)我们给出了图和超图的最大Steiner根连接方向的近似最小-最大关系的替代证明（由于Király和Lau(2008)[40]）。我们对图的近似最小-最大关系的证明绕过了纳什-威廉姆斯的强定向定理，并使用了为超图开发的工具。

{"title":"Splitting-off in hypergraphs","authors":"Kristóf Bérczi , Karthekeyan Chandrasekaran , Tamás Király , Shubhang Kulkarni","doi":"10.1016/j.jctb.2025.09.004","DOIUrl":"10.1016/j.jctb.2025.09.004","url":null,"abstract":"<div><div>The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lovász [47], [49] and Mader [50] showed the existence of this operation while preserving global and local connectivities respectively in graphs under certain conditions. These results have far-reaching applications in graph algorithms literature [3], [9], [10], [14], [19], [24], [25], [26], [27], [28], [31], [32], [34], [35], [37], [40], [42], [43], [48], [50], [51], [52], [53]. In this work, we introduce a splitting-off operation in hypergraphs. We show that there exists a local connectivity preserving complete splitting-off in hypergraphs and give a strongly polynomial-time algorithm to compute it in weighted hypergraphs. We illustrate the usefulness of our splitting-off operation in hypergraphs by showing two applications: (1) we give a constructive characterization of k-hyperedge-connected hypergraphs and (2) we give an alternate proof of an approximate min-max relation for max Steiner rooted-connected orientation of graphs and hypergraphs (due to Király and Lau (2008) [40]). Our proof of the approximate min-max relation for graphs circumvents the Nash-Williams' strong orientation theorem and uses tools developed for hypergraphs.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"176 ","pages":"Pages 319-383"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145265869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Connectoids I: A universal end space theory 连通线I：一个普适的端空间理论

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-06-27 DOI: 10.1016/j.jctb.2025.06.003

Nathan Bowler, Florian Reich

In this series we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects like undirected graphs, directed graphs, bidirected graphs, hypergraphs or finitary matroids.

In this paper we develop a universal end space theory based on connectoids: the end spaces of connectoids unify the existing end spaces of undirected and directed graphs and establish end spaces for bidirected graphs, hypergraphs and finitary matroids.

The main result shows that the tangle-like description of ends in undirected graphs, called directions, extends to connectoids: there is a one-to-one correspondence between the “directions” of a connectoid and its ends. Furthermore, we generalise normal trees of undirected graphs to connectoids and show that normal trees represent the ends of a connectoid as they do for undirected graphs.

在本系列中，我们介绍并研究了连通图的概念，它捕获了各种离散对象的连通性结构，如无向图、有向图、双向图、超图或有限拟阵。

引用次数: 0

Asymptotic half-grid and full-grid minors 渐近半格和全格子

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-10-22 DOI: 10.1016/j.jctb.2025.10.003

Sandra Albrechtsen, Matthias Hamann

We prove that every locally finite, quasi-transitive graph with a thick end whose cycle space is generated by cycles of bounded length contains the full-grid as an asymptotic minor and as a diverging minor. This in particular includes all locally finite Cayley graphs of finitely presented groups that are not virtually free, and partially solves problems of Georgakopoulos and Papasoglu and of Georgakopoulos and Hamann.

Additionally, we show that every (not necessarily quasi-transitive) graph of finite maximum degree which has a thick end and whose cycle space is generated by cycles of bounded length contains the half-grid as an asymptotic minor and as a diverging minor.

证明了每一个具有厚端的局部有限拟传递图，其循环空间是由有界长度的循环生成的，其全网格是渐近小格和发散小格。这尤其包括所有有限表示群的局部有限Cayley图，这些群不是几乎自由的，并且部分地解决了Georgakopoulos和Papasoglu以及Georgakopoulos和Hamann的问题。此外，我们还证明了每一个（不一定是拟传递的）有一个厚端且其循环空间由有界长度的循环生成的有限最大度图都包含半网格作为渐近次元和发散次元。

引用次数: 0

An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps 手性、可定向、自旋和不可定向旋转映射下的无限简单图族

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-10-16 DOI: 10.1016/j.jctb.2025.10.001

Isabel Hubard , Primož Potočnik , Primož Šparl

In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surface, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic products

C_{n} [m K_{1}]

, where

m \geq 3

n = s m

, with s an integer not divisible by 4. This answers a question posed by Wilson in 2002.

在本文中，我们提供了已知的第一个无限简单图族，每个简单图族都是手性映射的骨架，可定向表面上的自反射映射的骨架，以及不可定向表面上的自反射映射的骨架。这个族由所有字典积Cn[mK1]组成，其中m≥3，n=sm，其中s是不能被4整除的整数。这回答了威尔逊在2002年提出的一个问题。

引用次数: 0

Cubic graphs with no eigenvalues in the interval (−1,1) 在（−1,1）区间内无特征值的三次图

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B

Pub Date : 2026-01-01 Epub Date: 2025-11-05 DOI: 10.1016/j.jctb.2025.10.008

Krystal Guo , Gordon F. Royle

We give a complete characterization of the cubic graphs with no eigenvalues in the open interval

(- 1, 1)

. We first classify the connected cubic graphs with no eigenvalues in

(- 1, 1)

showing that there are two infinite families: one due to Guo and Mohar (2014) [7] and the other due to Kollár and Sarnak (2021) [12], and 13 “sporadic” graphs on at most 32 vertices. Then a not necessarily connected cubic graph has no eigenvalues in

(- 1, 1)

if and only if the same is true for every connected component. This classification allows us to show that

(- 1, 1)

is a maximal spectral gap set for cubic graphs, thereby answering a question of Kollár and Sarnak (2021) [12]. The techniques used include examination of the small subgraphs that can appear in such a graph and an application of the classification of generalized line graphs.

我们给出了开区间（- 1,1）上无特征值的三次图的完整刻划。我们首先对（- 1,1）中没有特征值的连通三次图进行分类，表明存在两个无限族：一个是由于Guo和Mohar(2014)[7]，另一个是由于Kollár和Sarnak(2021)[12]，以及13个“偶发”图，最多32个顶点。则一个不一定连通的三次图在（- 1,1）中没有特征值，当且仅当对每个连通分量都成立。这种分类使我们能够证明（−1,1）是三次图的最大谱间隙集，从而回答了Kollár和Sarnak(2021)[12]的问题。所使用的技术包括检查可能出现在这种图中的小子图和广义线形图分类的应用。

{"title":"Cubic graphs with no eigenvalues in the interval (−1,1)","authors":"Krystal Guo , Gordon F. Royle","doi":"10.1016/j.jctb.2025.10.008","DOIUrl":"10.1016/j.jctb.2025.10.008","url":null,"abstract":"<div><div>We give a complete characterization of the cubic graphs with no eigenvalues in the open interval <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math>. We first classify the connected cubic graphs with no eigenvalues in <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> showing that there are two infinite families: one due to Guo and Mohar (2014) [7] and the other due to Kollár and Sarnak (2021) [12], and 13 “sporadic” graphs on at most 32 vertices. Then a not necessarily connected cubic graph has no eigenvalues in <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> if and only if the same is true for every connected component. This classification allows us to show that <math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math> is a maximal spectral gap set for cubic graphs, thereby answering a question of Kollár and Sarnak (2021) [12]. The techniques used include examination of the small subgraphs that can appear in such a graph and an application of the classification of generalized line graphs.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"176 ","pages":"Pages 561-583"},"PeriodicalIF":1.2,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Journal of Combinatorial Theory Series B

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.

﹀