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 Hadwiger's conjecture for 3-arc graphs.
['David R. Wood', 'Guangjun Xu', 'Sanming Zhou']
Hadwiger's conjecture for 3-arc graphs