Tolerance graphs

Martin Charles Golumbic; Clyde L. Monma; William T. Trotter

doi:10.1016/0166-218X(84)90016-7

Tolerance graphs

Martin Charles Golumbic, Clyde L. Monma, William T. Trotter

Research output: Contribution to journal › Article › peer-review

Abstract

Tolerance graphs arise from the intersection of intervals with varying tolerances in a way that generalizes both interval graphs and permutation graphs. In this paper we prove that every tolerance graph is perfect by demonstrating that its complement is perfectly orderable. We show that a tolerance graph cannot contain a chordless cycle of length greater than or equal to 5 nor the complement of one. We also discuss the subclasses of bounded tolerance graphs, proper tolerance graphs, and unit tolerance graphs and present several possible applications and open questions.

Original language	English
Pages (from-to)	157-170
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	9
Issue number	2
DOIs	https://doi.org/10.1016/0166-218X(84)90016-7
State	Published - Oct 1984
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/0166-218X(84)90016-7

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title = "Tolerance graphs",

abstract = "Tolerance graphs arise from the intersection of intervals with varying tolerances in a way that generalizes both interval graphs and permutation graphs. In this paper we prove that every tolerance graph is perfect by demonstrating that its complement is perfectly orderable. We show that a tolerance graph cannot contain a chordless cycle of length greater than or equal to 5 nor the complement of one. We also discuss the subclasses of bounded tolerance graphs, proper tolerance graphs, and unit tolerance graphs and present several possible applications and open questions.",

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AB - Tolerance graphs arise from the intersection of intervals with varying tolerances in a way that generalizes both interval graphs and permutation graphs. In this paper we prove that every tolerance graph is perfect by demonstrating that its complement is perfectly orderable. We show that a tolerance graph cannot contain a chordless cycle of length greater than or equal to 5 nor the complement of one. We also discuss the subclasses of bounded tolerance graphs, proper tolerance graphs, and unit tolerance graphs and present several possible applications and open questions.

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Tolerance graphs

Abstract

ASJC Scopus subject areas

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