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K4-minor-free induced subgraphs of sparse connected graphs

par Joret, Gwenaël ;Wood, David
Référence SIAM journal on discrete mathematics, 32, 1, page (123-147)
Publication Publié, 2018

Article révisé par les pairs

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Résumé :

We prove that every connected graph G with m edges contains a set X of at most16 3 (m+1) vertices such that G−X has no K4 minor, or, equivalently, has treewidth at most 2. This bound is best possible. Connectivity is essential: If G is not connected, then only a bound of1 5m can be guaranteed.