the ramsey numbers of large trees versus wheels
نویسندگان
چکیده
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}.
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}.
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.
متن کاملThe Ramsey numbers of paths versus wheels
For two given graphsG1 andG2, the Ramsey numberR(G1,G2) is the smallest integer n such that for any graph G of order n, either G containsG1 or the complement of G containsG2. Let Pn denote a path of order n and Wm a wheel of order m+ 1. In this paper, we show that R(Pn,Wm)= 2n− 1 for m even and n m− 1 3 and R(Pn,Wm)= 3n− 2 for m odd and n m− 1 2. © 2004 Elsevier B.V. All rights reserved.
متن کاملOn Ramsey numbers for paths versus wheels
For two given graphs F and H, the Ramsey number R(F,H) is the smallest positive integer p such that for every graph G on p vertices the following holds: either G contains F as a subgraph or the complement of G contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Wm), where Pn is a path on n vertices and Wm is the graph obtained from a cycle on m vertices by adding a new ver...
متن کاملThe Ramsey Numbers of Paths Versus Wheels: a Complete Solution
Let G1 and G2 be two given graphs. The Ramsey number R(G1, G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or G contains a G2. We denote by Pn the path on n vertices and Wm the wheel on m + 1 vertices. Chen et al. and Zhang determined the values of R(Pn,Wm) when m 6 n + 1 and when n + 2 6 m 6 2n, respectively. In this paper we determine all the value...
متن کاملRamsey numbers of stars versus wheels of similar sizes
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.
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۴، صفحات ۸۷۹-۸۸۰
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