Elsevier

Discrete Mathematics

Volume 308, Issue 19, 6 October 2008, Pages 4389-4395
Discrete Mathematics

Planar Ramsey numbers for cycles

https://doi.org/10.1016/j.disc.2007.08.085Get rights and content
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Abstract

For two given graphs G and H the planar Ramsey number PR(G,H) is the smallest integer n such that every planar graph F on n vertices either contains a copy of G or its complement contains a copy H. By studying the existence of subhamiltonian cycles in complements of sparse graphs, we determine all planar Ramsey numbers for pairs of cycles.

MSC

05D10
05C55

Keywords

Ramsey number
Planar graph
Cycles

Cited by (0)

1

Research of the author supported in part by KBN Grant 2 P03A 015 23.