Discrete Applied Mathematics最新文献

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Construction, extension and paths of near-homogeneous tournaments 构建、扩展和路径近乎同质化的比赛

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.059

Rongxia Tang , Zhaojun Chen , Zan-Bo Zhang

A homogeneous tournament is a tournament with

4 t + 3

vertices such that every arc is contained in exactly

t + 1

cycles of length 3. Homogeneous tournaments are the first class of tournaments that are proved to be path extendable, which means that every nonhamiltonian path

P

in such a tournament

T

can be extended to a path

P^{'}

with the same initial and terminal vertex and

V (P^{'}) = V (P) \cup {u}

for a certain vertex

u \in V (T) ∖ V (P)

. In order to find more path extendable tournaments we study the generalization of homogeneous tournaments called near-homogeneous tournaments, in which every arc is contained in

t

t + 1

cycles of length 3. Near-homogeneity has been defined in tournaments with

4 t + 1

vertices. In this paper, we raise a new method to construct near-homogeneous tournaments with

4 t + 1

vertices. We then show that the definition of near-homogeneous tournament can be extended to tournaments with an even number of vertices. Finally we verify path extendability of near-homogeneous tournaments, thus expand the class of path extendable tournaments.

齐次比赛是指有4t+3个顶点的比赛，这样每个弧都包含在长度为3的t+1个循环中。齐次竞赛是第一类被证明是路径可扩展的竞赛，这意味着在这样一个竞赛T中的每一个非哈密顿路径P都可以被扩展到具有相同初始顶点和终点顶点的路径P '，并且对于某个顶点u∈V(T)∈V(P)∈V(P)∈V(P)≠V(P)∪{u}。为了找到更多路径可扩展的比赛，我们研究了齐次比赛的推广，称为近齐次比赛，其中每个弧都包含在t或t+1个长度为3的循环中。近同质性在4t+1个顶点的比赛中被定义。本文提出了一种构造具有4t+1个顶点的近齐次竞赛的新方法。然后，我们证明了近齐次比赛的定义可以扩展到具有偶数个顶点的比赛。最后，我们验证了近似同构竞赛的路径可扩展性，从而扩展了路径可扩展性竞赛的类别。

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引用次数: 0

Extremal distance spectra of graphs and essential connectivity 图的极值距离谱和基本连通性

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.070

Daoxia Zhang, Dan Li, Wenxiu Ding

A graph is trivial if it contains only one vertex. The essential connectivity of

G

, denoted by

κ^{'} (G)

, is the minimum number of vertices of

G

whose removal produces a disconnected graph with at least two non-trivial components. In this paper, we determine the

n

-vertex graph of given essential connectivity with minimum distance spectral radius. We also characterize the extremal graphs attaining the minimum distance spectral radius among all connected graphs with fixed essential connectivity and minimum degree. Furthermore, we characterize the extremal digraphs with minimum distance spectral radius among the strongly connected digraphs with given essential connectivity.

如果一个图只包含一个顶点，那么它是平凡的。G的基本连通性，用κ ' (G)表示，是G的最小顶点数，其移除会产生至少有两个非平凡分量的断开图。在本文中，我们确定了具有最小距离谱半径的给定基本连通的n顶点图。我们还描述了在所有具有固定基本连通性和最小度的连通图中获得最小距离谱半径的极值图。进一步，我们刻画了具有给定基本连通性的强连通有向图中具有最小距离谱半径的极值有向图。

引用次数: 0

Maximizing the number of maximal independent sets in graphs with a given matching number 具有给定匹配数的图中最大独立集的数量最大化

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.057

Xiaotong Gu, Hongzhi Deng, Yuting Tian, Jianhua Tu

In this paper, we determine the maximum number of maximal independent sets for three families of graphs. The first family comprises all 2-connected graphs with matching number

t

. The second family consists of all unicyclic graphs with matching number

t

. The third family encompasses all graphs on

n

vertices with matching number

t

where

2 t \leq n \leq 3 t

; note that the case

n \geq 3 t

has been settled in previous work.

在本文中，我们确定了三种图族的最大独立集的最大数目。第一族包含匹配数为t的所有2连通图，第二族包含匹配数为t的所有单环图，第三族包含匹配数为t的n个顶点上的所有图，其中2t≤n≤3t；注意，前面的工作已经解决了n≥3t的情况。

引用次数: 0

Forbidden configurations and dominating bicliques in undirected 2-quasi best match graphs 无向2-拟最优匹配图中的禁止构型和支配双链

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2026.01.001

Annachiara Korchmaros , Peter F. Stadler

2-quasi best match graphs (2qBMGs) are directed graphs that capture a notion of close relatedness in phylogenetics. Here, we investigate the underlying undirected graph of a 2qBMG (un2qBMG) and show that it contains neither a path

P_{l}

nor a cycle

C_{l}

of length

l \geq 6

as an induced subgraph. This property guarantees the existence of specific vertex decompositions with dominating bicliques that provide further insights into their structure.

2-准最佳匹配图（2qbmg）是有向图，它捕获了系统发育中近亲关系的概念。本文研究了一个2qBMG （un2qBMG）的底层无向图，证明了它既不包含路径Pl，也不包含长度为l≥6的循环Cl作为诱导子图。这个性质保证了特定顶点分解的存在，这些顶点分解具有主导曲线，可以进一步了解它们的结构。

引用次数: 0

Even cycle decompositions of the line graphs of cubic graphs 三次图的线形图的连循环分解

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-09 DOI: 10.1016/j.dam.2025.12.052

Chuixiang Zhou, Yuxi Zou

An even cycle decomposition of a graph is defined as a partition of its edges into cycles of even length. Let

G

be a 2-connected cubic graph. Markström conjectured that the line graph

L (G)

G

admits an even cycle decomposition. Suppose that

F = C_{1} \cup C_{2} \cup \dots \cup C_{k}

is a 2-factor of

G

, where each

C_{i}

(

1 \leq i \leq k

) is a cycle. Let

G_{F}

be the graph obtained from

G

by contracting each

C_{i}

(

1 \leq i \leq k

) to a vertex and deleting the resulting loops and parallel edges. In this paper, we prove that Markström’s conjecture is true if

G_{F}

is isomorphic to a tree for some 2-factor

F

G

图的偶环分解被定义为将图的边划分为偶数长度的环。设G是一个二连通三次图。Markström推测G的线形图L(G)允许偶循环分解。设F=C1∪C2∪⋯∪Ck是G的一个2因子，其中每个Ci（1≤i≤k）是一个循环。设GF为由G将每个Ci（1≤i≤k）缩并到一个顶点，并删除由此产生的环路和平行边得到的图。本文证明了如果GF同构于某2因子F (G)的树，则Markström的猜想是成立的。

引用次数: 0

Polarity on H-split graphs h -分裂图的极性

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.dam.2025.12.065

Fernando Esteban Contreras-Mendoza, César Hernández-Cruz

A partition

(A, B)

of the vertex set of a graph

G

is called a polar partition of

G

when

G [A]

and

\bar{G [B]}

are complete multipartite graphs. If

(A, B)

is a polar partition of

G

in which

G [A]

and

\bar{G [B]}

have at most

s

and

k

parts, respectively, then

(A, B)

is an

(s, k)

-polar partition of

G

, and

G

is said to be an

(s, k)

-polar graph. A graph is said to be unipolar (monopolar) if its vertex set admits a polar partition

(A, B)

such that

A

is a clique (an independent set, respectively). A graph admitting a

(1, 1)

-polar partition is usually called a split graph.

Naturally, most problems related to polar partitions are trivial on split graphs, even when some of them are very hard in general. In this work, we present some results related to polar partitions on two graph classes generalizing split graphs. Our main results include efficient algorithms to decide whether graphs in these classes admit such partitions. We also establish upper bounds on the order of minimal

(s, k)

-polar obstructions for these families, for any

s

and

k

(possibly

s = \infty

k = \infty

当G[A]和G[B]¯是完全多部图时，图G顶点集的划分（A，B）称为G的极划分。如果（A，B）是G的极分割，其中G[A]和G[B]¯分别最多有s和k个部分，则（A，B）是G的（s,k）极分割，G称为（s,k）极图。如果一个图的顶点集允许一个极分割（A，B），使得A是一个团（分别是一个独立的集合），那么这个图就是单极的（单极的）。具有（1,1）极分割的图通常称为分割图。当然，大多数与极坐标划分相关的问题在分割图上都是微不足道的，即使其中一些问题通常非常困难。在本文中，我们给出了关于两个图类的极坐标划分的一些结果。我们的主要成果包括有效的算法来决定这些类中的图是否允许这样的分区。对于任意s和k（可能是s=∞或k=∞），我们也建立了这些族的极小（s,k）极障碍的上界。

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引用次数: 0

On the (total) domination in subdivision graphs 关于细分图中的（总）支配

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.dam.2025.12.055

Esteban De Jesús Sánchez , Abel Cabrera-Martínez , Ismael Rios-Villamar , José M. Sigarreta

In this article, we study the total domination number and the

k

-domination number of the subdivision graph operator

S (G)

for simple graphs

G

. First, we obtain a closed formula for the total domination number of this well-known graph operator. Additionally, for

k \geq 2

, we obtain the exact value of the

k

-domination number of

S (G)

. The picture is notably different when considering the case

k = 1

, i.e., the domination number. In this case, we obtain some general bounds on the domination number of

S (G)

, which we further improve when

G

is a tree. Finally, we provide closed formulas for the domination number of the subdivision graph of some well-known composite graphs.

本文研究了简单图G的细分图算子S(G)的总支配数和k-支配数。首先，我们得到了这个著名图算子的总支配数的封闭公式。此外，当k≥2时，我们得到了S(G)的k支配数的确切值。当考虑k=1（即支配数）的情况时，情况明显不同。在这种情况下，我们得到了S(G)的支配数的一般界，当G是树时，我们进一步改进了这一界。最后，我们给出了一些著名的复合图的细分图的支配数的封闭公式。

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引用次数: 0

Vertex evaluation of multiplex graphs using Forman curvature 基于Forman曲率的多路图顶点评估

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.dam.2025.12.058

Taiki Yamada

The identification of vertices that play a central role in network analysis is a fundamental challenge. Although traditional centrality measures have been extensively employed for this purpose, the increasing complexity of modern networks necessitates the use of sophisticated metrics. The concept of Forman curvature has recently garnered significant attention as a promising approach. We define the Forman curvature for multiplex graphs, which are a category of complex networks characterized by multiple layers of connections between nodes. We then prove the key properties of the Forman curvature in the context of multiplex graphs and show its usefulness in identifying vertices occupying central positions within these networks. Moreover, through a series of comparative experiments with traditional graph features and graph kernels, we demonstrate that the Forman curvature can function as an effective metric for classifying the overall structure of networks.

识别在网络分析中起核心作用的顶点是一个根本性的挑战。虽然传统的中心性度量已被广泛用于此目的，但现代网络的日益复杂需要使用复杂的度量。福尔曼曲率的概念最近作为一种有前途的方法获得了极大的关注。我们定义了多路图的Forman曲率，多路图是一类以节点之间的多层连接为特征的复杂网络。然后，我们在多重图的背景下证明了Forman曲率的关键性质，并展示了它在识别这些网络中占据中心位置的顶点方面的有用性。此外，通过一系列与传统图特征和图核的对比实验，我们证明了Forman曲率可以作为对网络整体结构进行分类的有效度量。

引用次数: 0

Thick Forests 浓密的森林

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1016/j.dam.2025.12.042

Martin Dyer , Haiko Müller

We consider classes of graphs, which we call thick graphs, that have the vertices of a corresponding thin graph replaced by cliques and the edges replaced by cobipartite graphs. In particular, we consider the case of thick forests, which we show to be the largest class of perfect thick graphs.

Recognising membership of a class of thick

C

-graphs is NP-complete unless the class

C

is triangle-free, so we focus on this case. Even then membership can be NP-complete. However, we show that the class of thick forests can be recognised in polynomial time.

We consider two well-studied combinatorial problems on thick graphs, independent sets and proper colourings. Since determining the independence or chromatic number of a perfect graph is known to be tractable, we examine the complexity of counting all independent sets and colourings in thick forests.

Finally, we consider two parametric extensions to larger classes of thick graphs: where the parameter is the size of the thin graph, and where the parameter is its treewidth.

我们考虑一类图，我们称之为厚图，它们对应的薄图的顶点被团代替，边缘被二部图代替。特别地，我们考虑了浓密森林的情况，我们证明了它是最大的一类完美厚图。除非类C是无三角形的，否则识别一类厚C图的隶属性是np完全的，因此我们关注这种情况。即使这样，成员资格也可能是np完全的。然而，我们证明了厚森林的类别可以在多项式时间内识别。考虑两个研究得很好的关于厚图、独立集和适当着色的组合问题。由于确定完美图的独立性或色数是容易处理的，我们研究了在茂密的森林中计数所有独立集和着色的复杂性。最后，我们考虑两个参数扩展到更大的粗图类：其中参数是瘦图的大小，其中参数是它的树宽度。

引用次数: 0

A note on the second-largest number of dissociation sets in connected graphs 关于连通图中第二多解离集的注释

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics

Pub Date : 2026-01-07 DOI: 10.1016/j.dam.2025.12.045

Pingshan Li, Ke Yang, Wei Jin

A subset of vertices is called a dissociation set if it induces a subgraph with vertex degree at most one. Recently, Yuan et al. established the upper bound of the maximum number of dissociation sets among all connected graphs of order

n

and characterized the corresponding extremal graphs. They also proposed a question regarding the second-largest number of dissociation sets among all connected graphs of order

n

and the corresponding extremal graphs. In this paper, we give a positive answer to this question.

如果一个顶点的子集诱导出一个顶点度最多为1的子图，则称为解离集。最近Yuan等人建立了所有n阶连通图的最大解离集数的上界，并刻画了相应的极值图。他们还提出了一个关于在所有n阶连通图和相应的极值图中解离集数量第二的问题。本文对这一问题给出了肯定的回答。

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