Question 14
Given positive integers $k$ and $n$ ($n \ge 2$), find the minimum constant $c$ satisfying this assertion: if $G$ is a simple $kn$-regular graph (the degree of each vertex is $kn$) with $m$ vertices, then each vertex can be coloured one of $n$ colours, such that the number of “mono edges” is at most $cm$. Here, a mono edge is an edge incident to two vertices of the same colour.