Extremal Numbers for Odd Cycles

Zoltan Füredi, David S. Gunderson

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We describe the C 2k+1-free graphs on n vertices with maximum number of edges. The extremal graphs are unique for n ∈ {3k-1, 3k, 4k-2, 4k-1}. The value of ex(n, C2k+1) can be read out from the works of Bondy [3], Woodall [14], and Bollobás [1], but here we give a new streamlined proof. The complete determination of the extremal graphs is also new. We obtain that the bound for n 0(C 2k+1) is 4k in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turán graph.

Original languageEnglish
Pages (from-to)641-645
Number of pages5
JournalCombinatorics Probability and Computing
Volume24
Issue number4
DOIs
Publication statusPublished - Jul 1 2015

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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