Improved bounds for the graham-pollak problem for hypergraphs

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

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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
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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