G is a bipartite graph. Show G doesn't have an odd cycle. (Def. of odd cycle:...

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G is a bipartite graph. Show G doesn't have an odd cycle. (Def. of odd cycle:...

G is a bipartite graph. Show G doesn't have an odd cycle. (Def. of odd cycle: simple cycle w/ odd number of vertices)

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Answer 1

Answer #1

Proof. (⇒) If G is bipartite with bipartition X, Y of the vertices, then
any cycle C has vertices that must alternately be in X and Y . Thus,
since a cycle is closed, C must have an even number of vertices and hence is an even cycle .but not odd cycle

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Answer 2

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