The following are equivalent formulations of the definition of a bipartite graph:

  1. The vertices of the graph may be partitioned into two sets A and B, with all edges of the graph go from a vertex in A to a vertex in B. (This is flyingroc's definition above, and is the most common).
  2. The graph has chromatic number 2.
  3. All cycles (loops) in the graph have an even length.

The proofs of the equivalences are (as per mathematical custom) left as an exercise for the inclined reader.