Question

Prove that an undirected graph is bipartite iff it contains no cycle whose length is odd (called simply an "odd cycle").

An undirected graph G = (V,E) is called "bipartite" when the vertices can be
partitioned into two subsets V = V_1 u V_2 (with V_1 n V_2 = {}) such that
every edge of G has one endpoint in V_1 and the other in V_2 (equivalently,
no edge of G has both endpoints in V_1 or both endpoints in V_2).

Answer 1

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