A Note on the Ramsey Number of Even Wheels Versus Stars - Haghi Sh.; Maimani H.R. (Discussiones Mathematicae Graph Theory, 2018)
For two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N, such that for any graph on N vertices, either G contains G1 or Ḡ contains G2. Let Sn be a star of order n and Wm be a wheel of order m + 1. In this paper, we will show R(Wn, Sn) ≤ 5n/2 − 1, where n ≥ 6 is even. Also, by using this theorem, we conclude that R(Wn, Sn) = 5n/2 − 2 or 5n/2 −1, for n ≥ 6 and even. Finally, we prove that for sufficiently large even n we have R(Wn, Sn) = 5n/2 − 2.