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 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 ‾{G} 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.
Keywords:
Ramsey number, star, wheel, weakly pancyclic

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