J Austral Math Soc Ser A 50 pp204--212, 1991.

On r-Graphs and r-Multihypergraphs with Given Maximum Degree

Zoltán Füredi

(Received 15 April 1988; revised 12 April 1990)

Abstract

It is well known that if G is a multigraph (that is, a graph with multiple edges), the maximum number of pairwise disjoint edges in G is v(G) and its maximum degree is D(G), then |E(G)| £ vë3D/2û. We extend this theorem for r-graphs (that is, families of r-element sets) and for r-multihypergraphs (that is, r-graphs with repeated edges). Several problems remain open.

1980 AMS Subject Classification (1985 Revision): primary 05C65; secondary 05B40

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Authors

Zoltán Füredi: Mathematical Institute, Hungarian Academy of Sciences, 1364 Budapest POB 127, Hungary.

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Last Modified: Mon Feb 3 9:46:09 2003