Treewidth, Circle Graphs, and Circular Drawings

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-03-06 DOI:10.1137/22m1542854

Robert Hickingbotham, Freddie Illingworth, Bojan Mohar, David R. Wood

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 965-987, March 2024.
Abstract. A circle graph is an intersection graph of a set of chords of a circle. We describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the “usual suspects.” Our results imply that treewidth and Hadwiger number are linearly tied on the class of circle graphs and that the unavoidable induced subgraphs of a vertex-minor-closed class with large treewidth are the usual suspects if and only if the class has bounded rank-width. Using the same tools, we also study the treewidth of graphs [math] that have a circular drawing whose crossing graph is well-behaved in some way. In this setting, we show that if the crossing graph is [math]-minor-free, then [math] has treewidth at most [math] and has no [math]-topological minor. On the other hand, we show that there are graphs with arbitrarily large Hadwiger number that have circular drawings whose crossing graphs are 2-degenerate.

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树宽、圆图和圆形图画

SIAM 离散数学杂志》第 38 卷第 1 期第 965-987 页，2024 年 3 月。摘要圆图是圆的弦集的交集图。我们描述了具有大树宽的圆图不可避免的诱导子图。其中包括一些与 "常见图 "相去甚远的例子。我们的结果意味着，树宽和哈德维格数在圆图类上是线性关系，并且如果且仅如果具有大树宽的顶点-小封闭类具有有界的秩宽，则该类不可避免的诱导子图就是 "惯常嫌疑犯"。利用同样的工具，我们还研究了具有圆形图的图的树宽[math]，这些图的交叉图在某种程度上是良好的。在这种情况下，我们证明，如果交叉图是无[math]次要的，那么[math]的树宽至多为[math]，并且没有[math]拓扑次要。另一方面，我们证明了存在具有任意大的哈德维格数的图，这些图具有圆形图画，其交叉图是 2-退化的。

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.