Grid induced minor theorem for graphs of small degree

A graph H is an induced minor of a graph G if H can be obtained from G by vertex deletions and edge contractions. We show that there is a function f(k,d)=O(k10+2d5) so that if a graph has treewidth at least f(k,d) and maximum degree at most d, then it contains a k×k-grid as an induced minor. This pr...

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Vydané v:Journal of combinatorial theory. Series B Ročník 160; s. 206 - 214
Hlavný autor: Korhonen, Tuukka
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.05.2023
Predmet:
Grid
Induced minor
Treewidth
Induced minor
Grid
Treewidth
ISSN:0095-8956, 1096-0902
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Shrnutí:A graph H is an induced minor of a graph G if H can be obtained from G by vertex deletions and edge contractions. We show that there is a function f(k,d)=O(k10+2d5) so that if a graph has treewidth at least f(k,d) and maximum degree at most d, then it contains a k×k-grid as an induced minor. This proves the conjecture of Aboulker, Adler, Kim, Sintiari, and Trotignon (2021) [1] that any graph with large treewidth and bounded maximum degree contains a large wall or the line graph of a large wall as an induced subgraph. It also implies that for any fixed planar graph H, there is a subexponential time algorithm for maximum weight independent set on H-induced-minor-free graphs.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2023.01.002