Ramsey numbers of stars versus wheels of similar sizes
نویسنده
چکیده
We study the Ramsey number R(Wm, Sn) for a star Sn on n vertices and a wheel Wm on m + 1 vertices. We show that the Ramsey number R(Wm, Sn)= 3n− 2 for n=m,m+ 1, and m+ 2, where m 7 and odd. In addition, we give the following lower bound for R(Wm, Sn) where m is even: R(Wm, Sn) 2n+ 1 for all n m 6. © 2004 Elsevier B.V. All rights reserved.
منابع مشابه
The Ramsey numbers of large trees versus wheels
For two given graphs G1 and G2, the Ramseynumber R(G1,G2) is the smallest integer n such that for anygraph G of order n, either $G$ contains G1 or the complementof G contains G2. Let Tn denote a tree of order n andWm a wheel of order m+1. To the best of our knowledge, only R(Tn,Wm) with small wheels are known.In this paper, we show that R(Tn,Wm)=3n-2 for odd m with n>756m^{10}.
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متن کاملThe Ramsey numbers of stars versus wheels
For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Sn denote a star of order n and Wm a wheel of order m+1. This paper shows that R(Sn, W6) = 2n+1 for n ≥ 3 and R(Sn, Wm ) = 3n − 2 for m odd and n ≥ m − 1 ≥ 2. © 2003 Elsevier Ltd. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 292 شماره
صفحات -
تاریخ انتشار 2005