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Edge Separators for Graphs Excluding a Minor

par Joret, Gwenaël ;Lochet, Illiam;Seweryn, Micha̷l M.T.
Référence The electronic journal of combinatorics, 30, 4, 4.12
Publication Publié, 2023

Article révisé par les pairs

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Résumé :

We prove that every n-vertex Kt-minor-free graph G of maximum degree ∆ has a set F of (Math Presents) edges such that every component of G − F has at most n/2 vertices. This is best possible up to the dependency on t and extends earlier results of Diks, Djidjev, Sýkora, and Vrťo (1993) for planar graphs, and of Sýkora and Vrťo (1993) for bounded-genus graphs. Our result is a consequence of the following more general result: The line graph of G is isomorphic to a subgraph of the strong product (Math Presents) for some graph H with treewidth at most t − 2 and (Math Presents).