Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2008/r/2/iv/d/solution

Yes. Colour an even-parity vertex one colour and an odd-parity vertex the other. Every cube edge changes parity, so this is a proper two-colouring. At least two colours are needed because edges exist.

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