Decomposing the complete r -graph

• Main Authors: Leader, Imre, Milicevic, Luka, Tan, Ta Sheng
• Format: Article
• Published: Elsevier 2018
• Subjects: Q Science (General); QA Mathematics
• Online Access: http://eprints.um.edu.my/21539/; https://doi.org/10.1016/j.jcta.2017.08.008
• Institution: Universiti Malaya

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 asymptoti...