科研之友
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摘要
For k,l >= 1, a broom B-k,B-l is a tree on n = k+ l vertices obtained by connecting the central vertex of a star K-1,K-k with an end-vertex of a path on l - 1 vertices. As B-n-2,B-2 is a star and B-1,B-n-1 is a path, their Ramsey number have been determined among rarely known R(T-n) of trees T-n of order n. Erdos, Faudree, Rousseau and Schelp determined the value of R(B-k,B-l) for l >= 2k >= 2. We shall determine all other R(B-k,B-l) in this paper, which says that, for fixed n, R(B-n-l,B-l) decreases first on 1 <= l <= 2n/3 from 2n - 2 or 2n - 3 to [4n/3] - 1, and then it increases on,, 2n/3 < l <= n from inverted right perpendicular 4n/3 inverted left perpendicular - 1 to left perpendicalar 3n/2 right perpendicalar - 1. Hence R(Bn-ll) may attain the maximum and minimum values of R(T-n) as l varies.
- 出版日期2016-8-19
- 单位同济大学
