Induced subgraphs and tree decompositions XVI. Complete bipartite induced minors

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Induced subgraphs and tree decompositions XVII. Anticomplete sets of large treewidth

M Chudnovsky, S Hajebi, S Spirkl - arxiv preprint arxiv:2411.11842, 2024 - arxiv.org
Two sets $ X, Y $ of vertices in a graph $ G $ are" anticomplete" if $ X\cap Y=\varnothing $
and there is no edge in $ G $ with an end in $ X $ and an end in $ Y $. We prove that every …
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Induced subgraphs and tree decompositions XVIII. Obstructions to bounded pathwidth

M Chudnovsky, S Hajebi, S Spirkl - arxiv preprint arxiv:2412.17756, 2024 - arxiv.org
The pathwidth of a graph $ G $ is the smallest $ w\in\mathbb {N} $ such that $ G $ can be
constructed from a sequence of graphs, each of size at most $ w+ 1$, by gluing them …
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Treewidth versus clique number: induced minors

C Hilaire, M Milanič, N Trotignon, D Vasić - arxiv preprint arxiv …, 2024 - arxiv.org
arxiv:2410.17979v1 [math.CO] 23 Oct 2024 Treewidth versus clique number: induced minors
Page 1 arxiv:2410.17979v1 [math.CO] 23 Oct 2024 Treewidth versus clique number: induced …
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