On the Ramsey number of 4-cycle versus wheel - Enik Noviani; Edy Tri Baskoro (Indonesian Combinatorial Society (InaCombS), 2016)
For any fixed graphs G and H, the Ramsey number R(G,H) is the smallest positive integer n such that for every graph F on n vertices must contain G or the complement of F contains H. The girth of graph G is a length of the shortest cycle. A k-regular graph with the girth g is called a (k,g)-graph. If the number of of vertices in (k,g)-graph is minimized then we call this graph a (k,g)-cage. In this paper, we derive the bounds of Ramsey number R(C_4,W_n) for some values of n. By modifying (k, 5)-graphs, for k = 7 or 9, we construct these corresponding (C_4,W_n)-good graphs.