Authors: Sh. Haghi, H.R. Maimani Title: A note on the Ramsey number of even wheels versus stars Source: Discussiones Mathematicae Graph Theory Received 14.06.2016, Revised 01.12.2016, Accepted 01.12.2016, doi: 10.7151/dmgt.2009 | |
Abstract: For two graphs G_{1} and G_{2}, the Ramsey number R(G_{1},G_{2}) is the smallest integer N, such that for any graph on N vertices, either G contains G_{1} or ‾{G} contains G_{2}. Let S_{n} be a star of order n and W_{m} be a wheel of order m+1. In this paper, we will show R(W_{n}, S_{n})≤{5n/2-1}, where n≥{6} is even. Also, by using {this} theorem, we conclude that R(W_{n},S_{n})=5n/2-2 or 5n/2-1, for n≥{6} and even. Finally, we prove that for sufficiently large even n we have R(W_{n},S_{n})=5n/2-2. | |
Keywords: Ramsey number, star, wheel, weakly pancyclic | |
Links: |