Describe that a graph G is bipartite if and only if each circuit in G has even length. (A graph G = (V, E) is said to be bipartite if there is a partition V=V1unionV2, with V1intersectionV2 = 0, such that each edge had one endpoint in V1 and the other in V2. A distance between two vertices is the length of the shortest path connecting the vertices. The length of a path is the number of edges in it.)
Hint: Let v belong to V be a vertex. Consider the distances to v from each other vertex.