On the Ramsey number of the quadrilateral versus the book and the wheel
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.
Australasian Journal of Combinatorics
First Page Number
Last Page Number
Tse, Kung Kuen, "On the Ramsey number of the quadrilateral versus the book and the wheel" (2003). Kean Publications. 2670.