Hadwiger's conjecture for 3-arc graphs

David R. Wood, Guangjun Xu, Sanming Zhou

Published 2013-10-16, updated 2013-10-17Version 2

The 3-arc graph of a digraph $D$ is defined to have vertices the arcs of $D$ such that two arcs $uv, xy$ are adjacent if and only if $uv$ and $xy$ are distinct arcs of $D$ with $v\ne x$, $y\ne u$ and $u,x$ adjacent. We prove that Hadwiger's conjecture holds for 3-arc graphs.