Limits of dense graph sequences

L. Lovász, Balázs Szegedy

Research output: Contribution to journalArticle

288 Citations (Scopus)

Abstract

We show that if a sequence of dense graphs Gn has the property that for every fixed graph F, the density of copies of F in Gn tends to a limit, then there is a natural "limit object," namely a symmetric measurable function W : [0, 1]2 → [0, 1]. This limit object determines all the limits of subgraph densities. Conversely, every such function arises as a limit object. We also characterize graph parameters that are obtained as limits of subgraph densities by the "reflection positivity" property. Along the way we introduce a rather general model of random graphs, which seems to be interesting on its own right.

Original languageEnglish
Pages (from-to)933-957
Number of pages25
JournalJournal of Combinatorial Theory. Series B
Volume96
Issue number6
DOIs
Publication statusPublished - Nov 2006

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Graph in graph theory
Subgraph
Reflection Positivity
Measurable function
Symmetric Functions
Random Graphs
Tend
Object
Model

Keywords

  • Convergent graph sequence
  • Graph homomorphism
  • Limit
  • Quasirandom graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Limits of dense graph sequences. / Lovász, L.; Szegedy, Balázs.

In: Journal of Combinatorial Theory. Series B, Vol. 96, No. 6, 11.2006, p. 933-957.

Research output: Contribution to journalArticle

Lovász, L. ; Szegedy, Balázs. / Limits of dense graph sequences. In: Journal of Combinatorial Theory. Series B. 2006 ; Vol. 96, No. 6. pp. 933-957.
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