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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 513.05038

**Autor: ** Erdös, Paul

**Title: ** Ramsey numbers for brooms. (In English)

**Source: ** Combinatorics, graph theory and computing, Proc. 13th Southeast. Conf., Boca Raton 1982, Congr. Numerantium 35, 283-293 (1982).

**Review: ** [This article was published in the book announced in Zbl 504.00004.]

From the author's abstract: A broom B_{k,\ell} is a tree obtained by identifying an endvertex of a path on \ell vertices with the central vertex of star on k edges. The Ramsey number r(B_{k,\ell}) is determined precisely for \ell \geq 2k and relatively sharp bounds are found for 1 \leq \ell < 2k. For appropriate choices of k an \ell show r(B_{k,\ell} = **{**4(k+\ell)/3-1**}** which is the smallest possible value of the Ramsey number of any tree on k+\ell vertices.

**Reviewer: ** E.Palmer

**Classif.: ** * 05C55 Generalized Ramsey theory

05C05 Trees

**Keywords: ** Ramsey numbers of trees

**Citations: ** Zbl.504.00004

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