Past exam of the probability, statistics and options I course of the University of Oxford / 2007 / R / 1 / v

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- Solution v

Solution

True. Represent a vertex of

Q_{4}

by a four-bit string, with an edge changing exactly one bit. Color according to the parity of the sum of the bits. Every edge joins opposite parities, giving a proper two-coloring. Since the graph has edges, one color is impossible, so

χ (Q_{4}) = 2

.

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