Tree-width dichotomy

We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 103; p. 103517
Main Authors Lozin, Vadim, Razgon, Igor
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2022
Online AccessGet full text
ISSN0195-6698
1095-9971
DOI10.1016/j.ejc.2022.103517

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Summary:We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a tripod.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2022.103517