##
**Zentralblatt MATH**

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

**Zbl.No: ** 569.05041

**Autor: ** Erdös, Paul; Nesetril, J.; Rödl, Vojtech

**Title: ** Selectivity of hypergraphs. (In English)

**Source: ** Finite and infinite sets, 6th Hung. Combin. Colloq., Eger/Hung. 1981, Vol. I, Colloq. Math. Soc. János Bolyai 37, No.1, 265-284 (1984).

**Review: ** [For the entire collection see Zbl 559.00001.]

The concept of a selective hypergraph is introduced. Some results concerning the smallest number of edges needed for a selective k-graph are provided. They are similar to those for the B-property. It is shown that the minimal chromatic number of a selective graph H equals \chi(H) = (\chi(G)-1)(|V(G)|-1)+1. A construction of selective hypergraphs without short cycles is also given. The paper ends with the following result. For each K-graph G there exists a selective k-graph H with \chi(H) given by the formula above. Besides, if the edges e_{1},...,e_{q} form a cycle in H of length at most p \geq 2 then there exists a subgraph G' of H isomorphic to G, containing the edges e_{1},...,e_{q}.

**Reviewer: ** L.Zaremba

**Classif.: ** * 05C65 Hypergraphs

**Keywords: ** selective hypergraph; selective k-graph; chromatic number

**Citations: ** Zbl 559.00001

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag