Improved Bounds for Multicovering Hypergraphs
Abstract
The minimum number of bicliques needed to cover the edge set of the complete graph on n vertices is 2 n . The Graham-Pollak theorem states that at least n-1 bicliques are required to partition the edge set of the complete graph on n vertices. In this paper, we provide improvements for the generalizations of coverings of graphs and hypergraphs for some specific multiplicities. We also study an extension of the Katona-Szemerédi theorem to r-uniform hypergraphs.
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