Triangles in regular graphs with density below one half

  • Authors:

  • Allan siu lun Lo

  • Affiliations:

  • Department of pure mathematics and mathematical statistics, university of cambridge, cambridge cb3 0wb, uk (e-mail: allan.lo@cantab.net)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2009

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Abstract

Let k3reg(n, d) be the minimum number of triangles in d-regular graphs with n vertices. We find the exact value of k3reg(n, d) for d between $2n /5 + 12 \sqrt{n}/5$ and n/2. In addition, we identify the structure of the extremal graphs.