The typical structure of graphs without given excluded subgraphs

József Balogh, Béla Bollobás, Miklós Simonovits

Research output: Contribution to journalArticlepeer-review


Let L be a finite family of graphs. We describe the typical structure of L-free graphs, improving our earlier results (Balogh et al., J Combinat Theory Ser B 91 (2004), 1-24) on the Erdo{double acute}s- Frankl-Rödl theorem (Erdo{double acute}s et al., Graphs Combinat 2 (1986), 113-121), by proving our earlier conjecture that, for p = p(L) = min L∈L X(L) - 1, the structure of almost all L-free graphs is very similar to that of a random subgraph of the Turán graph T n,p. The "similarity" is measured in terms of graph theoretical parameters of L.

Original languageEnglish (US)
Pages (from-to)305-318
Number of pages14
JournalRandom Structures and Algorithms
Issue number3
StatePublished - May 2009


  • Extremal graphs
  • Graph counting
  • Structure of H-free graphs

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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