In a school assignment, I am to use contradiction to prove that if a graph is bipartite then all of its cycles have even order. In this context, what does it mean for a cycle to have even order? I tried using google and Wikipedia, but I am no closer to understanding what it means. Could you please explain it?
2026-03-28 22:26:32.1774736792
Order of cycles in graph
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Assume that $G$ contains only cycles of odd order. Then $G$ is not bipartite since the $V(G)$ cannot be partitioned into two partite sets, $U$ and $W$ such that the edges of $G$ join a vertex of $U$ to a vertex of $W$. Consider the $5$-cycle $C_5$ and this will be more clear.