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**Zentralblatt MATH**

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

**Zbl.No: ** 535.05049

**Autor: ** Erdös, Paul; Palka, Z.

**Title: ** Trees in random graphs. (In English)

**Source: ** Discrete Math. 46, 145-150 (1983); addendum ibid 48, 331 (1984).

**Review: ** The probability space consisting of all graphs on a set of n vertices where each edge occurs with probability p, independently of all other edges, is denoted by G(n,p). Theorem: For each \epsilon > 0 almost every graph G in G(n,p) is such if (1+\epsilon) log n/ log d < r < (2- \epsilon) log n/ log d where d = 1/(1-p), then G contains a maximal induced tree of order d. Problem: Let p be a function of n, find such a value of p for which a graph G in G(n,p) has the greatest induced tree.

**Reviewer: ** J.Mitchem

**Classif.: ** * 05C80 Random graphs

05C05 Trees

60C05 Combinatorial probability

**Keywords: ** induced star; maximal induced tree

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