Hadwiger's Conjecture for 3-Arc Graphs

David Wood, Guangjun Xu, Sanming Zhou

Abstract


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.


Keywords


Hadwiger's conjecture; Graph colouring; Graph minor; $3$-Arc graph

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