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 > nO(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)
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag