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.
| Comments: | 11 pages |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05C35, 68R10 |
| Cite as: | arXiv:2208.12589 [math.CO] |
| (or arXiv:2208.12589v2 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2208.12589 arXiv-issued DOI via DataCite |
From: Anand Babu N B [view email]
[v1]
Fri, 26 Aug 2022 11:30:26 UTC (25 KB)
[v2]
Fri, 22 May 2026 16:53:43 UTC (13 KB)
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