TY - JOUR
T1 - On the Ramsey number of the quadrilateral versus the book and the wheel
AU - Tse, Kung Kuen
PY - 2003
Y1 - 2003
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33645409756&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:33645409756
SN - 1034-4942
VL - 27
SP - 163
EP - 167
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
ER -