# bipartite graph - sufficient and necessary conditions

Sorry for a silly question, I got confused with the definition of bipartite graph.

What is a necessary and sufficient condition for a bipartite graph.

A bipartite graph has not odd circle


The above property defined as a sufficient conditions, does it mean that all possible even circles is absolutely eligible in bipartite graph?

It's of course a necessary condition, but I am not sure whether it is a sufficient.

What's wrong in the following graph with even circle?

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@fog: It is a bipartite graph: you just haven’t split the vertices correctly to show it. The correct vertex sets are $\{A,C\}$ and $\{B,D\}$. – Brian M. Scott Dec 26 '12 at 15:43