Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-29T03:30:27.995Z Has data issue: false hasContentIssue false
  • English
  • Français

The Cycle-Complete Graph Ramsey Numbers

Published online by Cambridge University Press:  11 April 2005

V. NIKIFOROV
V. NIKIFOROV
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, 38152, USA (e-mail: vnikifrv@memphis.edu)
Get access Rights & Permissions [Opens in a new window]

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
Information
Combinatorics, Probability and Computing , Volume 14 , Issue 3 , May 2005 , pp. 349 - 370
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)