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Durham University

Computer Science

Profile

Publication details for Dr George Mertzios

Mertzios, G.B. (2015). Multitolerance Graphs. In Encyclopedia of Algorithms. Kao, Ming-Yang Springer.

Author(s) from Durham

Abstract

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 | v ∈ V } of closed intervals on the real line and a set t = { tv | v ∈ V } of positive numbers, such that for any two vertices u, v ∈ V , uv ∈ E if and only if |Iu∩Iv|≥min{tu,tv}, where | I | denotes the length of the interval I.
Tolerance graphs have been introduced in [3], in order to generalize some of the well-known applications of interval graphs. If in the definition of tolerance graphs we replace the operation “min” between tolerances by “max,” we obtain the class of max-tolerance graphs [7]. Both tolerance and max-tolerance graphs have attracted many research efforts (e.g., [4, 5, 7–10]) as they find numerous applications, especially i ...