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

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