A note on tolerance graph recognition

  title={A note on tolerance graph recognition},
  author={Ryan B. Hayward and Ron Shamir},
  journal={Discrete Applied Mathematics},
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 ={ v | v∈V} of positive real numbers such that (x; y)∈E ⇔ |Ix∩ Iy|¿min{ x; y}. We show that every tolerance graph has a polynomial size integer representation. It follows that tolerance graph recognition is in NP. c © 2004 Elsevier B.V. All rights reserved.