I am stuck on this problem and need help figuring it out. Here are some of my thoughts:
- A bipartite graph contains no odd cycle.
- Every n odd cycle is a minor of n+1 even cycle.
2026-03-25 13:13:35.1774444415
Prove that every graph is a minor of a bipartite graph.
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Here are some hints:
Let $G$ be a graph on $n$ vertices. We want to show that it is a minor of some bipartite graph. To this end, consider $K_{n,n}$. $K_{n,n}$ contains $K_n$ as a minor (why?), and as $K_n$ contains $G$ as a minor (why?), $K_{n,n}$ contains $G$ as a minor (why?).