Decomposing the complete r -graph
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...
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| Format: | Article |
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Elsevier
2018
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| Summary: | 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. |
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