Leader, Imre and Milicevic, Luka and Tan, Ta Sheng (2018) Decomposing the complete r -graph. Journal of Combinatorial Theory, Series A, 154. pp. 21-31. ISSN 0097-3165, DOI https://doi.org/10.1016/j.jcta.2017.08.008.
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Official URL: https://doi.org/10.1016/j.jcta.2017.08.008
Abstract
Let fr(n) be the minimum number of complete r-partite r-graphs needed to partition the edge set of the complete r-uniform hypergraph on n vertices. Graham and Pollak showed that f2(n)=n−1. An easy construction shows that fr(n)≤(1−o(1))(n⌊r/2⌋) and it has been unknown if this upper bound is asymptotically sharp. In this paper we show that fr(n)≤([formula presented]+o(1))(nr/2) for each even r≥4.
| Item Type: | Article |
|---|---|
| Funders: | UNSPECIFIED |
| Uncontrolled Keywords: | Hypergraph; Decomposition; Graham–Pollak |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 26 Jun 2019 03:22 |
| Last Modified: | 26 Jun 2019 03:22 |
| URI: | http://eprints.um.edu.my/id/eprint/21539 |
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