Hadwiger's Conjecture with Certain Forbidden Induced Subgraphs

Abstract

We prove that $\{\overline{K_3},H\}$-free graphs are not counterexamples to Hadwiger's Conjecture, where $H$ is any one of 33 graphs on seven, eight, or nine vertices, or $H=K_8$. This improves on past results of Plummer-Stiebitz-Toft, Kriesell, and Bosse. The proofs are mostly computer-assisted.

24 pages, 5 figures