English

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

Computational Complexity 2022-10-25 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2205.09076,
  title  = {On the complexity of recognizing Stick, BipHook and Max Point-Tolerance graphs},
  author = {Irena Rusu},
  journal= {arXiv preprint arXiv:2205.09076},
  year   = {2022}
}

Comments

24 pages, 12 figures

R2 v1 2026-06-24T11:21:22.961Z