The typical structure of graphs without given excluded subgraphs

József Balogh, Béla Bollobás, M. Simonovits

Research output: Article

28 Citations (Scopus)

Abstract

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
Pages (from-to)305-318
Number of pages14
JournalRandom Structures and Algorithms
Volume34
Issue number3
DOIs
Publication statusPublished - máj. 2009

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ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics

Cite this

The typical structure of graphs without given excluded subgraphs. / Balogh, József; Bollobás, Béla; Simonovits, M.

In: Random Structures and Algorithms, Vol. 34, No. 3, 05.2009, p. 305-318.

Research output: Article

Balogh, József ; Bollobás, Béla ; Simonovits, M. / The typical structure of graphs without given excluded subgraphs. In: Random Structures and Algorithms. 2009 ; Vol. 34, No. 3. pp. 305-318.
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