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?