title: Interval Graph Limits.
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 functionW(x,y) on the unit square, withxandyuniform on the interval (0, 1). Instead, we fix aWand change the underlying distribution of the coordinatesxandy. 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.
authors.affiliation: Department of Mathematics, Stanford University, Stanford, CA 94305, USA.
authors.forename: Persi
authors.initials: P
authors.lastname: Diaconis
authors.affiliation: Department of Statistics, Stanford University, Stanford, CA 94305, USA.
authors.forename: Susan
authors.initials: S
authors.lastname: Holmes
authors.affiliation: Department of Mathematics, Uppsala University, P.O. Box 480, Uppsala, Sweden.
authors.forename: Svante
authors.initials: S
authors.lastname: Janson
keywords: graph limits; intersection graphs; interval graphs