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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: Leader, Imre, Tan, Ta Sheng
Format: Article
Published: Australian National University 2018
Subjects:
Q Science (General)
QA Mathematics
Online Access:http://eprints.um.edu.my/21540/
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p4/pdf
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spelling my.um.eprints.215402019-06-26T03:32:56Z http://eprints.um.edu.my/21540/ Improved bounds for the graham-pollak problem for hypergraphs Leader, Imre Tan, Ta Sheng Q Science (General) QA Mathematics 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. Australian National University 2018 Article PeerReviewed 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 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p4/pdf
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic Q Science (General)
QA Mathematics
spellingShingle Q Science (General)
QA Mathematics
Leader, Imre
Tan, Ta Sheng
Improved bounds for the graham-pollak problem for hypergraphs
description 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.
format Article
author Leader, Imre
Tan, Ta Sheng
author_facet Leader, Imre
Tan, Ta Sheng
author_sort Leader, Imre
title Improved bounds for the graham-pollak problem for hypergraphs
title_short Improved bounds for the graham-pollak problem for hypergraphs
title_full Improved bounds for the graham-pollak problem for hypergraphs
title_fullStr Improved bounds for the graham-pollak problem for hypergraphs
title_full_unstemmed Improved bounds for the graham-pollak problem for hypergraphs
title_sort improved bounds for the graham-pollak problem for hypergraphs
publisher Australian National University
publishDate 2018
url http://eprints.um.edu.my/21540/
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p4/pdf
_version_ 1643691588300308480
score 13.211869

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