Question 38
Find the largest positive integer $k$ for which there exists a convex polyhedron $P$ with the following properties:
(a) $P$ has exactly $2022$ edges.
(b) The degrees of the vertices of $P$ don't differ by more than $1$.
(c) It is possible to colour the edges of $P$ with $k$ colours such that for every colour $c$, and every pair of vertices ($v_1$, $v_2$) of $P$, there is a monochromatic path between $v_1$ and $v_2$ in the colour $c$.
(a) $P$ has exactly $2022$ edges.
(b) The degrees of the vertices of $P$ don't differ by more than $1$.
(c) It is possible to colour the edges of $P$ with $k$ colours such that for every colour $c$, and every pair of vertices ($v_1$, $v_2$) of $P$, there is a monochromatic path between $v_1$ and $v_2$ in the colour $c$.