DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 23(1) (2003) 141-158
DOI: 10.7151/dmgt.1191

THE RAMSEY NUMBER r(C7,C7,C7)

Ralph Faudree

Department of Mathematical Science
University of Memphis
Memphis, TN 38152, USA
e-mail: RFaudree@memphis.edu

Annette Schelten and Ingo Schiermeyer

Fakultät für Mathematik und Informatik
Technische Universität Bergakademie Freiberg
09596 Freiberg, Germany
e-mail: Annette.Schelten@t-online.de
e-mail: Schierme@math.tu-freiberg.de

Abstract

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.

Keywords: Ramsey numbers, extremal graphs.

2000 Mathematics Subject Classification: 05C55, 05C35.

References

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Received 30 July 2001
Revised 18 January 2002