A weak form of Hadwiger's conjecture

Dominic van der Zypen

Published 2013-12-10, updated 2013-12-12Version 3

We introduce the following weak version of Hadwiger's conjecture: If $G$ is a graph and $\kappa$ is a cardinal such that there is no coloring map $c:G \to \kappa$, then $K_\kappa$ is a minor of $G$. We prove that this statement is true for graphs with infinite chromatic number