Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24145
Title: The planar Ramsey number PR(C4, K8)
Authors: Chen, Y
Cheng, TCE 
Zhang, Y
Zhou, G
Keywords: Clique
Planar graph
Quadrilateral
Ramsey number
Issue Date: 2014
Publisher: Elsevier
Source: Discrete applied mathematics, 2014, v. 171, p. 28-34 How to cite?
Journal: Discrete Applied Mathematics 
Abstract: For two given graphs G1 and G2, the planar Ramsey number PR(G1,G2) is the smallest integer N such that for any planar graph G on N vertices, either G contains G1 or its complement contains G2. Let Cn denote a cycle of length n and Kl a complete graph of order l. Sun, Yang, Lin and Song conjectured that PR(C4,Kl)=3l + ⌊(l-1)/5⌋-2 and the conjecture was proved for l7. In this paper, it is shown that PR(C 4, K8)=23 which confirms the conjecture for l=8.
URI: http://hdl.handle.net/10397/24145
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.02.002
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