On a problem in extremal graph theory

D. T. Busolini, P. Erdös

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 - Jan 1 1977

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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