Extremal Graphs with Bounded Densities of Small Subgraphs

Jerrold R. Griggs, M. Simonovits, George Rubin Thomas

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let Ex(n, k, μ) denote the maximum number of edges of an n-vertex graph in which every subgraph of k vertices has at most μ edges. Here we summarize some known results of the problem of determining Ex(n, k, μ), give simple proofs, and find some new estimates and extremal graphs. Besides proving new results, one of our main aims is to show how the classical Turán theory can be applied to such problems. The case μ = (k2) - 1 is the famous result of Turán.

Original languageEnglish
Pages (from-to)185-207
Number of pages23
JournalJournal of Graph Theory
Volume29
Issue number3
Publication statusPublished - Nov 1998

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Extremal Graphs
Subgraph
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Graph in graph theory
Vertex of a graph
Estimate

Keywords

  • Dirac's Theorem
  • Extremal graphs
  • Turán's Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Extremal Graphs with Bounded Densities of Small Subgraphs. / Griggs, Jerrold R.; Simonovits, M.; Thomas, George Rubin.

In: Journal of Graph Theory, Vol. 29, No. 3, 11.1998, p. 185-207.

Research output: Contribution to journalArticle

Griggs, JR, Simonovits, M & Thomas, GR 1998, 'Extremal Graphs with Bounded Densities of Small Subgraphs', Journal of Graph Theory, vol. 29, no. 3, pp. 185-207.
Griggs, Jerrold R. ; Simonovits, M. ; Thomas, George Rubin. / Extremal Graphs with Bounded Densities of Small Subgraphs. In: Journal of Graph Theory. 1998 ; Vol. 29, No. 3. pp. 185-207.
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