Disproof of the group coloring version of the Hadwiger conjecture

Abstract

Inspired by the idea of Barát, Joret and Wood for disproving the list Hadwiger conjecture [The Electronic Journal of Combinatorics 18 (2011), P232], we disprove the group coloring version of the Hadwiger conjecture, which asserts that if G is a Kk-minor-free graph, then χg(G) ≤ k, where χg(G) denotes the group chromatic number of G.