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