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- Title
A NOTE ON THE RAMSEY NUMBER OF EVEN WHEELS VERSUS STARS.
- Authors
HAGHI, SH.; MAIMANI, H. R.
- 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 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.
- Subjects
RAMSEY numbers; INTEGERS; STAR graphs (Graph theory); GEOMETRIC vertices; EDGES (Geometry)
- Publication
Discussiones Mathematicae: Graph Theory, 2018, Vol 38, Issue 2, p397
- ISSN
1234-3099
- Publication type
Article
- DOI
10.7151/dmgt.2009