Suppose that G is a graph with chromatic number k 2 and that there is given a k-coloring

Chapter 14, Problem 21

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Suppose that G is a graph with chromatic number k 2 and that there is given a k-coloring of G using the colors {1, 2, . . . , k}. Prove or disprove: For every two distinct colors i, j {1, 2, . . . , k}, there are adjacent vertices of G colored i and j.

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