The Ramsey Numbers R(Tn, W6) for Small n∗
نویسندگان
چکیده
Let Tn denote a tree of order n and Wm a wheel of order m + 1. Baskoro et al. conjectured in [2] that if Tn is not a star, then R(Tn,Wm) = 2n − 1 for m ≥ 6 even and n ≥ m− 1. We disprove the Conjecture in [6]. In this paper, we determine R(Tn,W6) for n ≤ 8 which is the first step for us to determine R(Tn,W6) for any tree Tn.
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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