 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2007/r/1/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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