\b[Both are bipartite.] Partition the <vertices> by <parity> of the number of one bits. A cube <edge> changes one bit and an interior diagonal changes three bits, so both types join opposite <parity> classes. In fact $Q'_3$ is $K_{4,4}$: from any <vertex> its three cube neighbors and its opposite <vertex> exhaust the four <vertices> of opposite <parity>.

Solution

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

 Solution (source code)