Annals of Combinatorics

, Volume 17, Issue 1, pp 27–52 | Cite as

Interval Graph Limits

  • Persi Diaconis
  • Susan HolmesEmail author
  • Svante Janson


We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W(x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits.

Mathematics Subject Classification

60C05 (68P10) 


interval graphs graph limits intersection graphs 


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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of StatisticsStanford UniversityStanfordUSA
  3. 3.Department of MathematicsUppsala UniversityUppsalaSweden

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