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The Cycle-Complete Graph Ramsey Numbers
Published online by Cambridge University Press: 11 April 2005
Abstract
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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 $p\,{\geq}\,4r+2$.
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- © 2005 Cambridge University Press
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