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arXiv · 2208.12589

Improved Bounds for Multicovering Hypergraphs

Anand Babu·Sundar Vishwanathan
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Abstract

The minimum number of bicliques needed to cover the edge set of the complete graph on $n$ vertices is $\lceil \log_2 n \rceil$. 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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BibTeXRIS

Anand Babu, Sundar Vishwanathan. 2026-05-22. Improved Bounds for Multicovering Hypergraphs. https://arxiv.org/abs/2208.12589

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