The cycle-complete graph Ramsey number r(C₅,K₇)

• Autorzy: Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

The cycle-complete graph Ramsey number r(Cₘ,Kₙ) is the smallest integer N such that every graph G of order N contains a cycle Cₘ on m vertices or has independence number α(G) ≥ n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r(Cₘ,Kₙ) = (m-1)(n-1)+1 for all m ≥ n ≥ 3 (except r(C₃,K₃) = 6). This conjecture holds for 3 ≤ n ≤ 6. In this paper we will present a proof for r(C₅,K₇) = 25.

Słowa kluczowe

EN

Ramsey numbers; extremal graphs

Kategorie tematyczne

• 05C35: Extremal problems
• 05C55: Generalized Ramsey theory

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 129-139

Daty

wydano

2005

otrzymano

2003-11-06

poprawiono

2005-02-16

Twórcy

autor

Ingo Schiermeyer

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

Bibliografia

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• [12] V. Rosta, On a Ramsey Type Problem of J.A. Bondy and P. Erdős, I & II, J. Combin. Theory (B) 15 (1973) 94-120, doi: 10.1016/0095-8956(73)90035-X.
• [13] I. Schiermeyer, All Cycle-Complete Graph Ramsey Numbers r(Cₘ, K₆), J. Graph Theory 44 (2003) 251-260, doi: 10.1002/jgt.10145.
• [14] Y.J. Sheng, H.Y. Ru and Z.K. Min, The value of the Ramsey number R(Cₙ,K₄) is 3(n-1) +1 (n ≥ 4), Australas. J. Combin. 20 (1999) 205-206.
• [15] A. Thomason, private communication.

Identyfikatory

DOI

10.7151/dmgt.1267