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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| Published in: | Journal of combinatorial theory. Series B Vol. 160; pp. 206 - 214 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
01.05.2023
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| Subjects: | |
| ISSN: | 0095-8956, 1096-0902 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0095-8956 1096-0902 |
| DOI: | 10.1016/j.jctb.2023.01.002 |