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7:17 AM
Bookmarking for myself to update the links in these answers
27
Q: When does a graph underlie the Hasse diagram of a poset?

Ethan SplaverFor any finite poset $P=(X,\leq)$ there is a graph $G$ underlying its Hasse diagram $H=(X,\lessdot)$, so that $V(G)=X$ and $E(G)=\{\{u,v\}:u\lessdot v\}$. With that said, is it possible to characterize all these graphs? That is, those graphs which underlie the Hasse diagram of some finite poset? ...

 

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