Oriol Serra1
Let be a finite set of integers. The distance graph
has the set
of integers as vertices and two vertices at distance
are adjacent
in
. A conjecture of Xuding Zhu states that if the chromatic number of
achieves its maximum value
then the graph has a clique of
order
. We prove that the chromatic number of a distance graph with
is five if and only if either
or
. This confirms Zhu's conjecture for
.