On a problem in extremal graph theory

D. T. Busolini, P. Erdős

Research output: Contribution to journalArticle

Abstract

The number T*(n,k) is the least positive integer such that every graph with n = (2k+1) + t vertices (t ≥ 0) and at least T*(n,k) edges contains k mutually vertex-disjoint complete subgraphs S1, S2,..., Sk where Si has i vertices, 1 ≤ i ≤ k. Obviously T*(n, k) ≥ T(n, k), the Turán number of edges for a Kk. It is shown that if n ≥ 9 8k2 then equality holds and that there is ε{lunate} > 0 such that for (2k+1) ≤ n ≤ (2k+1) + ε{lunate}k2 inequality holds. Further T*(n, k) is evaluated when k > k0(t).

Original languageEnglish
Pages (from-to)251-254
Number of pages4
JournalJournal of Combinatorial Theory. Series B
Volume23
Issue number2-3
DOIs
Publication statusPublished - 1977

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Extremal Graph Theory
Graph theory
Subgraph
Disjoint
Equality
Integer
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

On a problem in extremal graph theory. / Busolini, D. T.; Erdős, P.

In: Journal of Combinatorial Theory. Series B, Vol. 23, No. 2-3, 1977, p. 251-254.

Research output: Contribution to journalArticle

Busolini, D. T. ; Erdős, P. / On a problem in extremal graph theory. In: Journal of Combinatorial Theory. Series B. 1977 ; Vol. 23, No. 2-3. pp. 251-254.
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