Tolerance graphs

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)157-170
Number of pages14
JournalDiscrete Applied Mathematics
Issue number2
StatePublished - Oct 1984
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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