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Is there any theorem that apllies to non simple cycles and chromatic number? For example we know that x(G)=2 if G does not contains odd cycles. What about a non-simple cycle that contains odd cycles. E.g A square and a triangle having a common vertex is (n=6,3-chromatic) A petagon and a triangle having a common vertex is (n=7, 3-chromatic) Is any proof for saying that at least 3 colors are needed to use for non simple cycles that contain an odd cycle?And is that related to the number of its vertices? PS it is not a homework but basic to use it for one Thnx in advance

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