The tripartite Ramsey number for trees
نویسندگان
چکیده
We prove that for every ε > 0 there are α > 0 and n0 ∈ N such that for all n ≥ n0 the following holds. For any two-colouring of the edges of Kn,n,n one colour contains copies of all trees T of order k ≤ (3− ε)n/2 and with maximum degree ∆(T ) ≤ n. This answers a conjecture of Schelp.
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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عنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 34 شماره
صفحات -
تاریخ انتشار 2009