Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole.
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A clock is a graph consisting of an induced cycle C and a vertex not in C with at least two non-adjacent neighbours in C. We show that every clock-free graph of large treewidth contains a "basic obstruction" of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall.
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© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
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Except where otherwise noted, this item's license is described as Attribution 4.0 International