On the complexity of recognizing Stick, BipHook and Max Point-Tolerance graphs

Stick graphs are defined as follows. Let A (respectively B) be a set of vertical horizontal) segments in the plane such that bottom endpoints and left B lie on same ground line with slope −1. The graph by B, which is necessarily bipartite, intersection B. We answer an open problem showing recognizing NP-complete. This result allows us to easily solve two other problems, namely recognition BipHook max point-tolerance graphs. show both them NP-complete problems.