\b[False.] The <complete bipartite graph> $K_{3,3}$ has <chromatic number> two, but is nonplanar. For example a simple bipartite plane graph has $e\leq2v-4$, because all facial cycles have length at least four; $K_{3,3}$ has $v=6$, $e=9>8$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 1 / 17F / i / Solution

 Solution (source code)