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I'm trying to prove that a Hamilton path is the only topological sort. I think I need to show that in case there are two topological sorts, none of them is a Hamilton path.

How can I prove that a Hamilton path is the only topological sort in a DAG?

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The main thing you need to observe is that an Hamilton path is a path that goes through all vertices. Think how can one dag have 2 different topological sorts

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