Edge Separators for Graphs Excluding a Minor

Abstract

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).