A Weak form of Hadwiger’s Conjecture Pages 170-172

A Weak form of Hadwiger’s Conjecture
Pages 170-172
Dominic van der Zypen

DOI: http://dx.doi.org/10.6000/1927-5129.2014.10.23

Published: 25 April 2014

Abstract: We introduce the following weak version of Hadwiger’s conjecture: If image003 is a graph and is a cardinal such that there is no coloring map image009 then image012 is a minor of image003 . We prove that this statement is true for graphs with infinite chromatic number.

Keywords: Graph theory, graph colouring, graph minors, Hadwiger’s conjecture