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Pré-Publication, Document De Travail Année : 2022

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

Irena Rusu

Résumé

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.

Dates et versions

hal-03831538 , version 1 (27-10-2022)

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Irena Rusu. On the complexity of recognizing Stick, BipHook and Max Point-Tolerance graphs. 2022. ⟨hal-03831538⟩
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