The Excluded Tree Minor Theorem Revisited

Abstract

AbstractWe prove that for every tree $T$ of radius $h$ , there is an integer $c$ such that every $T$ -minor-free graph is contained in $H\boxtimes K_c$ 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.