The extremal function for K9 minors

Abstract

We prove that every (simple) graph on n ≥ 9 vertices and at least 7n - 27 edges either has a K9 minor, or is isomorphic to K2,2,2,3,3 or is isomorphic to a graph obtained from disjoint copies of K1,2,2,2,2,2 by identifying cliques of size six. The proof of one of our lemmas is computer-assisted. © 2005 Elsevier Inc. All rights reserved.