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8. The graph coloring problem is the problem of finding the small- est number of colors such that when each vertex is assigned a color,
8. The graph coloring problem is the problem of finding the small- est number of colors such that when each vertex is assigned a color, no two adjacent vertices have the same color. Any graph can be greedily colored in the following way. Denote the colors by 1,2,3,.... Process the vertices in any order and assign to each vertex the smallest color available. (a) Prove that if the graph has maximum degree vertex d, then
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