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**Zentralblatt MATH**

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

**Zbl.No: ** 842.05046

**Autor: ** Erdös, Paul; Tuza, Zsolt

**Title: ** Vertex coverings of the edge set in a connected graph. (In English)

**Source: ** Alavi, Y. (ed.) et al., Graph theory, combinatorics, algorithms and applications. Vol. 2. Proceedings of the seventh quadrennial international conference on the theory and applications of graphs, Kalamazoo, MI, USA, June 1-5, 1992. New York, NY: Wiley, 1179-1187 (1995).

**Review: ** We prove that every connected graph with n vertices and m edges contains a set of at most ^{2}/_{7} (m+n+1) vertices that meets all edges. This bound is best possible in general, as shown by an infinite family of connected graphs.

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C65 Hypergraphs

05C70 Factorization, etc.

**Keywords: ** vertex coverings; transversal; transversal number; hypergraph; connected graph; bound

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag