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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my.um.eprints.215392019-06-26T03:22:22Z http://eprints.um.edu.my/21539/ Decomposing the complete r -graph Leader, Imre Milicevic, Luka Tan, Ta Sheng Q Science (General) QA Mathematics 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. Elsevier 2018 Article PeerReviewed 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 https://doi.org/10.1016/j.jcta.2017.08.008 doi:10.1016/j.jcta.2017.08.008 |
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Q Science (General) QA Mathematics Leader, Imre Milicevic, Luka Tan, Ta Sheng Decomposing the complete r -graph |
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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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Article |
| author |
Leader, Imre Milicevic, Luka Tan, Ta Sheng |
| author_facet |
Leader, Imre Milicevic, Luka Tan, Ta Sheng |
| author_sort |
Leader, Imre |
| title |
Decomposing the complete r -graph |
| title_short |
Decomposing the complete r -graph |
| title_full |
Decomposing the complete r -graph |
| title_fullStr |
Decomposing the complete r -graph |
| title_full_unstemmed |
Decomposing the complete r -graph |
| title_sort |
decomposing the complete r -graph |
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Elsevier |
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2018 |
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http://eprints.um.edu.my/21539/ https://doi.org/10.1016/j.jcta.2017.08.008 |
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