Graphs with large maximum degree containing no odd cycles of a given length

  • Authors:

  • Paul Balister;Béla Bollobás;Oliver Riordan;Richard H. Schelp

  • Affiliations:

  • Department of Mathematical Sciences, University of Memphis, Memphis, TN;Department of Mathematical Sciences, University of Memphis, Memphis, TN and Trinity College, Cambridge CB2 1TQ, UK;Trinity College, Cambridge CB2 1TQ, UK;Department of Mathematical Sciences, University of Memphis, Memphis, TN

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2003

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Abstract

Let us write f (n, Δ; C2k+1) for the maximal number of edges in a graph of order n and maximum degree Δ that contains no cycles of length 2k+ 1. For n/2 ≤ Δ ≤ n - k- 1 and n sufficiently large we show that f (n, Δ;C2k-1) = Δ (n - Δ), with the unique extremal graph a complete bipartite graph.