I would like to know if there are nice criteria to know if the ordered complex $C$ induced by a poset is contractible. I am also interested in the same question for subcomplexes of $C$.
$C$ happens to be a flag complex, and I found that all induced subcomplexes are contractible iff the underlying graph of $C$ is chordal.
However, this doesn't fit my purposes.
Do you know any result in this respect?