The Treewidth and Pathwidth of Graph Unions

IF 0.9 3区数学 Q2 MATHEMATICS SIAM Journal on Discrete Mathematics Pub Date : 2024-01-10 DOI:10.1137/22m1524047

Bogdan Alecu, Vadim V. Lozin, Daniel A. Quiroz, Roman Rabinovich, Igor Razgon, Viktor Zamaraev

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 261-276, March 2024.
Abstract. Given two [math]-vertex graphs [math] and [math] of bounded treewidth, is there an [math]-vertex graph [math] of bounded treewidth having subgraphs isomorphic to [math] and [math]? Our main result is a negative answer to this question, in a strong sense: we show that the answer is no even if [math] is a binary tree and [math] is a ternary tree. We also provide an extensive study of cases where such “gluing” is possible. In particular, we prove that if [math] has treewidth [math] and [math] has pathwidth [math], then there is an [math]-vertex graph of treewidth at most [math] containing both [math] and [math] as subgraphs.

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图元的树宽和路径宽

SIAM 离散数学杂志》，第 38 卷第 1 期，第 261-276 页，2024 年 3 月。摘要。给定两个有界树宽的[math]顶点图[math]和[math]，是否存在一个有界树宽的[math]顶点图[math]，其子图与[math]和[math]同构？我们的主要结果从强意义上否定了这个问题：我们证明，即使 [math] 是二叉树，[math] 是三叉树，答案也是否定的。我们还对这种 "粘合 "可能发生的情况进行了广泛研究。特别是，我们证明了如果[math]的树宽是[math]，而[math]的路径宽是[math]，那么就存在一个树宽至多为[math]的[math]顶点图，它同时包含[math]和[math]这两个子图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.

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