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

Irena Rusu

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arXiv · 2205.09076

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

Irena Rusu

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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.

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Irena Rusu. 2022-05-18. On the complexity of recognizing Stick, BipHook and Max Point-Tolerance graphs. https://arxiv.org/abs/2205.09076

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