  For $D$ being a subset of positive integers, the integer distance graph is
the graph $G(D)$, whose vertex set is the set of integers, and edge set is the
set of all pairs $uv$ with $|u-v| \in D$. It is known that $\chi(G(D)) \leq
|D|+1$.
  This article studies the problem (which is motivated by a conjecture of Zhu):
"Is it true that $\chi(G(D)) = |D|+1$ implies $\omega(G(D)) \geq |D|+1$, where
$\omega(H)$ is the clique number of $H$?". We give a negative answer to this
question, by showing an infinite class of integer distance graphs with
$\chi(G(D))=|D|+1$ but $\omega(G(D))=|D|-1$.
