Authors: Leader, Imre
Milićević, Luka 
Tan, Ta Sheng
Title: Decomposing the complete r-graph
Journal: Journal of Combinatorial Theory. Series A
Volume: 154
First page: 21
Last page: 31
Issue Date: 1-Feb-2018
Rank: M21
ISSN: 0097-3165
DOI: 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.
Keywords: Decomposition | Graham–Pollak | Hypergraph
Publisher: Elsevier
Project: Ministry of Higher Education of Malaysia, FRGS grant FP048-2014B

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