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Interval Graph Limits

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Persi Diaconis

  2. Department of Statistics, Stanford University, Stanford, CA, 94305, USA

    Susan Holmes

  3. Department of Mathematics, Uppsala University, P.O. Box 480, Uppsala, Sweden

    Svante Janson

Authors
  1. Persi Diaconis
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  2. Susan Holmes
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  3. Svante Janson
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Correspondence to Susan Holmes.

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Diaconis, P., Holmes, S. & Janson, S. Interval Graph Limits. Ann. Comb. 17, 27–52 (2013). https://doi.org/10.1007/s00026-012-0175-0

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  • DOI: https://doi.org/10.1007/s00026-012-0175-0

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