Unformatted text preview: be incident with at least one of them, but then some vertex is incident with two edges, contradicting no adjacent edges. 20. (a) [BB] E degvi = 5(4) + 2(2) = 24 = 21£1, so there are 12 edges. (b) E deg Vi = 4(3) + 2(4) + 2(5) = 30 = 21£1, so there are 15 edges. 21. (a) [BB] This is not bipartite because it contains a triangle. (b) This is bipartite with bipartition sets indicated R and W on the graph at the left below. R W R W R BJ W R w~w R W R (c) [BB] This is bipartite with bipartition sets indicated R and W on the graph at the right above. (d) This is not bipartite. Consider the vertices labeled 1, 2, 3, 4, 5 in the picture at the left below. Vertices 1 and 2 are would have to lie in different bipartition sets and, thus, 1 and 3 would lie in the same set. Since 3 and 4, and 4 and 5 lie in different sets, 3 and 5 lie in the same set. But this...
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 Summer '10
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 Graph Theory, Vertex, loop, vertices, R W R W R

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