Table of Contents
ISRN Algebra
Volume 2011 (2011), Article ID 926191, 10 pages
http://dx.doi.org/10.5402/2011/926191
Research Article

The Cycle-Complete Graph Ramsey Number π‘Ÿ ( 𝐢 9 , 𝐾 8 )

1Department of Mathematics, Yarmouk University, Irbid 21163, Jordan
2Department of Mathematics, Statistics, and Physics, Qatar University, Doha, Qatar

Received 11 May 2011; Accepted 14 June 2011

Academic Editor: R. L. Soto

Copyright © 2011 M. S. A. Bataineh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It has been conjectured by Erdős, Faudree, Rousseau, and Schelp that π‘Ÿ ( 𝐢 π‘š , 𝐾 𝑛 ) = ( π‘š βˆ’ 1 ) ( 𝑛 βˆ’ 1 ) + 1 for all ( π‘š , 𝑛 ) β‰  ( 3 , 3 ) satisfying that π‘š β‰₯ 𝑛 β‰₯ 3 (except π‘Ÿ ( 𝐢 3 , 𝐾 3 ) = 6 ) . In this paper, we prove this for the case π‘š = 9 and 𝑛 = 8 .