The Ramsey number r(C₇,C₇,C₇)

• Autorzy: Ralph Faudree , Annette Schelten , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.

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: 2003
• Tom: 23
• Numer: 1
• Strony: 141-158

Daty

wydano

2003

otrzymano

2001-07-30

poprawiono

2002-01-18

Twórcy

autor

Ralph Faudree

• Department of Mathematical Science, University of Memphis, Memphis, TN 38152, USA

autor

Annette Schelten

• Fakultät für Mathematik und Informatik, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany

autor

Ingo Schiermeyer

• Fakultät für Mathematik und Informatik, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany

Bibliografia

• [1] A. Bialostocki and J. Schönheim, On Some Turan and Ramsey Numbers for C₄, Graph Theory and Combinatorics, Academic Press, London, (1984) 29-33.
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• [5] V. Chvátal, On Hamiltonian's Ideals, J. Combin. Theory (B) 12 (1972) 163-168.
• [6] C. Clapham, The Ramsey Number r(C₄,C₄,C₄), Periodica Mathematica Hungarica 18 (1987) 317-318.
• [7] P. Erdős, On the Combinatorial Problems which I would most Like to See Solved, Combinatorica 1 (1981) 25-42.
• [8] R.J. Faudree and R.H. Schelp, All Ramsey Numbers for Cycles in Graphs, Discrete Math. 8 (1974) 313-329.
• [9] R.E. Greenwood and A.M. Gleason, Combinatorial Relations and Chromatic Graphs, Canadian J. Math. 7 (1995) 1-7.
• [10] T. Łuczak, R(Cₙ,Cₙ,Cₙ) ≤ (4+o(1))n, J. Combin. Theory (B) 75 (1999) 174-187.
• [11] S.P. Radziszowski, Small Ramsey Numbers, Electronic J. Combin. 1 (1994) update 2001.
• [12] A. Schelten, Bestimmung von Ramsey-Zahlen zweier und dreier Graphen (Dissertation, TU Bergakademie Freiberg, 2000).
• [13] P. Rowlinson amd Yang Yuangsheng, On the Third Ramsey Numbers of Graphs with Five Edges, J. Combin. Math. and Combin. Comp. 11 (1992) 213-222.
• [14] P. Rowlinson and Yang Yuangsheng, On Graphs without 6-Cycles and Related Ramsey Numbers, Utilitas Mathematica 44 (1993) 192-196.

Identyfikatory

DOI

10.7151/dmgt.1191