The Excluded Tree Minor Theorem Revisited

DOI10.1017/S0963548323000275arXiv2303.14970MaRDI QIDQ6509351

Author name not available (Why is that?)

Abstract: We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

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