Finitely forcible graphons

L. Lovász, B. Szegedy

Research output: Contribution to journalArticle

23 Citations (Scopus)


We investigate families of graphs and graphons (graph limits) that are determined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one element, i.e., a unique structure is forced by finitely many subgraph densities. Generalizing results of Turán, Erd"s-Simonovits and Chung-Graham-Wilson, we construct numerous finitely forcible graphons. Most of these fall into two categories: one type has an algebraic structure and the other type has an iterated (fractal-like) structure. We also give some necessary conditions for forcibility, which imply that finitely forcible graphons are "rare", and exhibit simple and explicit non-forcible graphons.

Original languageEnglish
Pages (from-to)269-301
Number of pages33
JournalJournal of Combinatorial Theory. Series B
Issue number5
Publication statusPublished - Sep 1 2011



  • Extremal graph
  • Finitely forcible graphon
  • Graph limit
  • Graphon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this