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A note on tolerance graph recognition

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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⇔|IxIy|⩾min{τx,τy}. We show that every tolerance graph has a polynomial size integer representation. It follows that tolerance graph recognition is in NP.

Keywords

Tolerance graph
Tolerance representation
Class NP

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The first author acknowledges the support of NSERC. The second author was supported in part by the Israeli Science Foundation founded by the Israeli Academy of Sciences and Humanities (Grant 309/02).