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arXiv · 1605.04730

$K_{4}$-Minor-Free Induced Subgraphs of Sparse Connected Graphs

Gwenaël Joret·David R. Wood
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Abstract

We prove that every connected graph $G$ with $m$ edges contains a set $X$ of at most $\frac{3}{16}(m + 1)$ vertices such that $G-X$ has no $K_4$ 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 of $\frac{1}{5}m$ can be guaranteed.

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Gwenaël Joret, David R. Wood. 2016-05-17. $K_{4}$-Minor-Free Induced Subgraphs of Sparse Connected Graphs. https://doi.org/10.1137/16m107712x

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