Induced subgraphs and tree decompositions II. Toward walls and their line graphs in graphs of bounded degree
JOURNAL OF COMBINATORIAL THEORY SERIES B(2024)
Abstract
This paper is motivated by the following question: what are the unavoidable induced subgraphs of graphs with large treewidth? Aboulker et al. made a conjecture which answers this question in graphs of bounded maximum degree, asserting that for all k and Delta, every graph with maximum degree at most Delta and sufficiently large treewidth contains either a subdivision of the (k xk)-wall or the line graph of a subdivision of the (k x k)-wall as an induced subgraph. We prove two theorems supporting this conjecture, as follows.
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Key words
Induced Subgraph,Tree decomposition,Treewidth
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