Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Multitolerance Graphs

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_684-1

Years and Authors of Summarized Original Work

2011; Mertzios

Problem Definition

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. A graph G = (V, E) on n vertices is a tolerance graph if there exists a collection I = { Iv | vV } of closed intervals on the real line and a set t = { tv | vV } of positive numbers, such that for any two vertices u, vV , uvE if and only if \(\vert I_{u} \cap I_{v}\vert \geq \min \{ t_{u},t_{v}\}\)

Keywords

Multitolerance graphs Tolerance graphs Intersection model Minimum coloring Maximum clique Maximum-weight independent set 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Engineering and Computing SciencesDurham UniversityDurhamUK