3 problems

Let an interval catch digraph (ICD) be a digraph represented by intervals on a line, with an arc determined by one interval's catch point lying in another interval. Let a central-m…

Minimal unbounded tolerance representation conjecture. Every minimally unbounded tolerance graph has a tolerance representation with exactly one unbounded vertex.

Golumbic–Monma–Trotter conjecture. The intersection of cocomparability graphs with tolerance graphs is exactly the class of bounded tolerance graphs.