{c}

The <complete bipartite graph> $K_{3,3}$ is connected, simple, and has no triangles because all its cycles have even length. It has $n=6$ <vertices> and $m=9$ <edges>. A planar drawing would require $9\leq2\cdot6-4=8$ by part (i), a contradiction. Therefore \b[$K_{3,3}$ is nonplanar].

Solution

Past exam of the probability, statistics and options I course of the University of Oxford / 2010 / R / 1 / ii / a / Solution

 Solution (source code)