# Proving that a planar graph is bipartite [duplicate]

Let $G$ be a connected planar graph with a planar embedding where every face boundary is a cycle of even length. Prove that $G$ is bipartite.

It is quite easy to prove the converse, but how to do this? My line of thought is to assume an odd cycle and show a contradiction, but I don't know where to head? This is homework, so please give hints only, not a full solution.

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