On the Ramsey number of the quadrilateral versus the book and the wheel

Document Type

Article

Publication Date

12-1-2003

Abstract

Let G and H be graphs. The Ramsey number R(G, H) is the least integer such that for every graph F of order R(G, H), either F contains G or F contains H. Let Bn and Wn denote the book graph K2+Kn and the wheel graph K1 + Cn-1, respectively. In 1978, Faudree, Rousseau and Sheehan computed R(C4, Bn) for n ≤ 8. In this paper, we compute R(C4,Bn) for 8 ≤ n ≤ 12 and R(C4,Wn) for 4 ≤ n ≤ 13. In particular, we find that R(C4, B8) = 17, not 16 as claimed in 1978 by Faudree, Rousseau and Sheehan. Most of the results are based on computer algorithms.

Publication Title

Australasian Journal of Combinatorics

First Page Number

163

Last Page Number

167

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