As established above, $Q'_3\cong K_{4,4}$. Select any three <vertices> in each <parity> class; all nine <edges> between the two triples are present, giving a $K_{3,3}$ subgraph. A <planar graph> has only planar subgraphs, whereas $K_{3,3}$ is nonplanar by the permitted result. Therefore $\boxed{Q'_3\text{ is nonplanar}}$.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2008 / R / 2 / v / Solution

 Solution (source code)