All cycle-complete graph Ramsey numbers r(Cm, K6)

  • Authors:

  • Ingo Schiermeyer

  • Affiliations:

  • Institut für Diskrete Mathematik und Algebra, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2003

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Abstract

The cycle-complete graph Ramsey numberr(Cm, Kn) is thesmallest integer N such that every graph G of orderN contains a cycle Cm on m verticesor has independence number ±(G) e n. It hasbeen conjectured by Erdõs, Faudree, Rousseau and Schelp thatr(Cm, Kn) = (m -1) (n - 1) + 1 for all m ≥ n ≥ 3 (exceptr(C3, K3) = 6). Thisconjecture holds for 3 d n ≤ 5. In this paper we willpresent a proof for n = 6 and for all n e 7 withm ≥ n2 - 2n. © 2003 WileyPeriodicals, Inc. J Graph Theory 44: 251260, 2003