树独立性编号 I. 无(偶数孔、菱形、金字塔)图形

IF 0.9 3区 数学 Q2 MATHEMATICS
Tara Abrishami, Bogdan Alecu, Maria Chudnovsky, Sepehr Hajebi, Sophie Spirkl, Kristina Vušković
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引用次数: 0

摘要

树独立数(tree-independence number)最早由达拉德(Dallard)、米拉尼奇(Milanič)和斯托格尔(Štorgel)定义和研究,是树宽的一种变体,专门用于解决最大独立集问题。在一系列论文中,阿布里萨米等人提出了所谓的中心袋法,用于研究有界树宽的诱导障碍。其中,他们证明了在(偶数洞、菱形、金字塔)无簇图的某一超类中,树宽受簇数函数的约束。在本文中,我们放宽了有界小群数假设,并证明有界.通过已有的结果,我们得到了该类图中最大权重独立集问题的多项式时间算法。我们的结果还证实了 Dallard、Milanič 和 Štorgel 对该类图的猜想,即在遗传图类中,当且仅当树宽受有界小群数的函数约束时,树宽才是有界的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tree independence number I. (Even hole, diamond, pyramid)-free graphs

The tree-independence number tree- α , first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so-called central bag method to study induced obstructions to bounded treewidth. Among others, they showed that, in a certain superclass C of (even hole, diamond, pyramid)-free graphs, treewidth is bounded by a function of the clique number. In this paper, we relax the bounded clique number assumption, and show that C has bounded tree- α . Via existing results, this yields a polynomial-time algorithm for the Maximum Weight Independent Set problem in this class. Our result also corroborates, for this class of graphs, a conjecture of Dallard, Milanič, and Štorgel that in a hereditary graph class, tree- α is bounded if and only if the treewidth is bounded by a function of the clique number.

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来源期刊
Journal of Graph Theory
Journal of Graph Theory 数学-数学
CiteScore
1.60
自引率
22.20%
发文量
130
审稿时长
6-12 weeks
期刊介绍: The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .
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