Improved bounds for the graham-pollak problem for hypergraphs
For a fixed r, let fr(n) denote the minimum number of complete r-partite r- graphs needed to partition the complete r-graph on n vertices. The Graham-Pollak theorem asserts that f2(n) = n – 1. An easy construction shows that [formula presented], and we write cr for the least number such that [formul...
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| Main Authors: | , |
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| Format: | Article |
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Australian National University
2018
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| Subjects: | |
| Online Access: | http://eprints.um.edu.my/21540/ https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p4/pdf |
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| Summary: | For a fixed r, let fr(n) denote the minimum number of complete r-partite r- graphs needed to partition the complete r-graph on n vertices. The Graham-Pollak theorem asserts that f2(n) = n – 1. An easy construction shows that [formula presented], and we write cr for the least number such that [formula presented] It was known that cr < 1 for each even r ≥ 4, but this was not known for any odd value of r. In this short note, we prove that c295 < 1. Our method also shows that cr → 0, answering another open problem. |
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