The Ramsey numbers of trees versus W6 or W7

  • Authors:

  • Yaojun Chen;Yunqing Zhang;Kemin Zhang

  • Affiliations:

  • Department of Mathematics, Nanjing University, Nanjing, China;Department of Mathematics, Nanjing University, Nanjing, China;Department of Mathematics, Nanjing University, Nanjing, China

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2006

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Abstract

Let Tn denote a tree of order n and Wm a wheel of order m + 1. In this paper, we show the Ramsey numbers R(Tn, W6) = 2n - 1 + µ for n ≥ 5, where µ = 2 if Tn = Sn, µ = 1 if Tn = Sn(1, 1) or Tn = Sn(1, 2) and n ≡ 0 (mod 3), and µ = 0 otherwise; R(Tn, W7) = 3n - 2 for n ≥ 6.