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**Zentralblatt MATH**

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

**Zbl.No: ** 209.28004

**Autor: ** Erdös, Paul; Gerencsér, L.; Máté, A.

**Title: ** Problems of graph theory concerning optimal design (In English)

**Source: ** Combinat. Theory Appl., Colloquia Math. Soc. János Bolyai 4, 317-325 (1970).

**Review: ** [For the entire collection see Zbl 205.00201.]

Let G be a connected graph. f(G,k) is the smallest integer for which there exists a set of f(G,k) vertices of G so that every vertex of G is joined to at least one of these vertices by a path of length \leq k. The principal results of the authors state as follows: Let G have diameter \leq 2k. Then f(G,K) \leq \sqrt{n log n+o(n)}. Further for every d < 2^{-3/2} there is a graph of n > n_{O}(d) vertices and diameter two for which f(G,k) > d \sqrt{n log n}.

**Classif.: ** * 05C99 Graph theory

05B30 Other designs, configurations

**Citations: ** Zbl 205.00201(EA)

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