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I'm drawing it and I'm having trouble finding the two sets. Could someone give me a drawing with colorings of a cycle with even length such that it is bipartite? Also, could someone provide a proof of whether every even cycle is bipartite? I already know that a bipartite graph has no odd cycles.

EDIT: I just figured it out with $C_4$. Could someone still provide a proof whether all $C_n$ is bipartite?

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    Start at some vertex, go through the cycle and color every second vertex in this color. You need "even" so that once you walked through the cycle completely things fit together. If you have difficulty writing a formal proof if this let me know. – quid Oct 21 '17 at 13:36
  • Okay that makes sense. If you could show that with proper notation, I'll be happy to award you the answer. –  Oct 21 '17 at 13:37
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    Here is a more general question with an argument: https://math.stackexchange.com/questions/311665/proof-a-graph-is-bipartite-if-and-only-if-it-contains-no-odd-cycles – quid Oct 21 '17 at 13:46
  • Ok then my question is answered. Should I delete this question? –  Oct 21 '17 at 13:52
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    I marked it as a duplicate instead. If you prefer it is deleted, let me know. – quid Oct 21 '17 at 14:19

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