Please someone give me the clear idea about dilworth theorem for graph or DAG. I read about it in multiple places but more I am reading getting more confusing. So please someone help me to understand it properly.
Thanks in advance.
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Applicated to a DAG, it says that we can find divide the set of vertices into subsets V1, ..., Vk, so that any two vertices in any subset are reachable one from another (in one direction, of course), and then choose , so that none of vi are reachable from any other.