If G is any bipartite graph, then every circuit in G has an even number of edges.
G is any bipartite graph.
Given that G is bipartite.
Let X and Y are the two sets of vertices.
Since G is bipartite, every step alone a walk takes you either from X to Y or from Y to X...
If G is any graph with at least two vertices and if G does not have a circuit with an odd number of edges, the G is bipartite.
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