I'm in the midst of some doctoral research and trying to figure out a particularly tricky reduction. I think my best shot is to reduce from an NP-complete problem on posets, if one exists.
I did some digging but did not find anything NP-complete; I found a couple of items that are FPT with respect to the diameter of the poset, but I don't think that's terribly helpful in my search.
I know I may not find anything here, but I figure it doesn't hurt to ask. Does anyone know of any NP-complete problems on posets?