2022/05/18 by Irena Rusu, Rusu, Irena
Computer Science · Environmental Science · #Computational Geometry and Mesh Generation #Remote Sensing and LiDAR Applications
paper · pdf · doi:10.48550/arxiv.2205.09076
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.