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The Cycle-Complete Graph Ramsey Numbers

Published online by Cambridge University Press:  11 April 2005

V. NIKIFOROV
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, 38152, USA (e-mail: vnikifrv@memphis.edu)

Abstract

In 1978 Erdős, Faudree, Rousseau and Schelp conjectured that \[ r ( C_{p},K_{r} ) = ( p-1 ) (r-1) +1 \] for every $p\,{\geq}\,r\,{\geq}\,3$, except for $p\,{=}\,q\,{=}\,3$. This has been proved for $r\,{\leq}\,6$, and for \[ p \geq r^{2}-2r\].

In this note we prove the conjecture for $p\,{\geq}\,4r+2$.

Type
Paper
Copyright
© 2005 Cambridge University Press

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