# 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

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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