Dilworth's theorem
= Dilworth's theorem
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{title2=$\text{minimum chain partition size}=\text{maximum antichain size}$}
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= Dilworth theorem
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Every finite <partially ordered set> can be partitioned into as many <chains in a partial order> as its largest <antichain>. Reachability in an acyclic <directed graph> is a <partial order>, so the theorem supplies chains which can be expanded into directed paths, possibly overlapping at intervening vertices.