The number of graphs without forbidden subgraphs

József Balogh, Béla Bollobás, M. Simonovits

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

Given a family ℒ of graphs, set p =p(ℒ) = minℒ∈ℒ χ(L) - 1 and, for n≥ 1, denote by P(n,ℒ) the set of graphs with vertex set [n] containing no member of ℒ as a subgraph,and write ex(n,ℒ) for the maximal size of a member of P(n, ℒ). Extending a result of Erdos, Frankl and Rödl (Graphs Combin. 2 (1986) 113), we prove that A figure is presented. For some constant γ = γ(ℒ) > 0, and characterize γ in terms of some related extremal graph problems. In fact, if ex(n,ℒ) = O(n2-δ), then any γ

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of Combinatorial Theory. Series B
Volume91
Issue number1
DOIs
Publication statusPublished - May 2004

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Forbidden Subgraph
Graph in graph theory
Extremal Graphs
Erdös
Subgraph
Figure
Denote
Vertex of a graph

Keywords

  • Erdos-Kleitman-Rothschild theory
  • Extremal graphs
  • Speed function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

The number of graphs without forbidden subgraphs. / Balogh, József; Bollobás, Béla; Simonovits, M.

In: Journal of Combinatorial Theory. Series B, Vol. 91, No. 1, 05.2004, p. 1-24.

Research output: Contribution to journalArticle

Balogh, József ; Bollobás, Béla ; Simonovits, M. / The number of graphs without forbidden subgraphs. In: Journal of Combinatorial Theory. Series B. 2004 ; Vol. 91, No. 1. pp. 1-24.
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