Leader, Imre and Tan, Ta Sheng
(2018)
*Improved bounds for the graham-pollak problem for hypergraphs.*
Electronic Journal of Combinatorics, 25 (1).
#P1.4.
ISSN 1077-8926

Official URL: https://www.combinatorics.org/ojs/index.php/eljc/a...

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | Decomposition; Graham-Pollak; Hypergraph |

Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |

Divisions: | Faculty of Science > Institute of Mathematical Sciences |

Depositing User: | Ms. Juhaida Abd Rahim |

Date Deposited: | 26 Jun 2019 03:32 |

Last Modified: | 26 Jun 2019 03:32 |

URI: | http://eprints.um.edu.my/id/eprint/21540 |

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