A note on tolerance graph recognition

Authors:
Ryan B. Hayward;Ron Shamir
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alta., Canada T6G 2E8;School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 5
Cited 4

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Abstract

A graph G=(V,E) is a tolerance graph if there is a set I={Iv|v ∈ V} of closed real intervals and a set τ = {τv|v ∈ V} of positive real numbers such that (x, y) ∈ E ⇔ |Ix ∩ Iy| ≥ min{τx, τy}. We show that every tolerance graph has a polynomial size integer representation. It follows that tolerance graph recognition is in NP.