A note on tolerance graph recognition Original Research Article

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.