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Abstract
In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if n divides (nk), then the complete k-uniform hypergraph on n vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence v1,e1,v2,...,vn,en of distinct vertices vi and distinct edges e i so that each e i contains vi and vi+1. So the divisibility condition is clearly necessary. In this note, we prove that the conjecture holds whenever k ® 4 and n ® 30. Our argument is based on the Kruskal-Katona theorem. The case when k = 3 was already solved by Verrall, building on results of Bermond.
Original language | English |
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Pages (from-to) | 128-135 |
Number of pages | 8 |
Journal | Journal of Combinatorial Theory, Series A |
Volume | 126 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Berge cycles
- Hamilton cycles
- Hamilton decompositions
- Hypergraphs
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
- Computational Theory and Mathematics
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Dive into the research topics of 'Decompositions of complete uniform hypergraphs into Hamilton Berge cycles'. Together they form a unique fingerprint.Projects
- 1 Finished
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Edge-Colourings and Hamilton Decompostitions of Graphs
Engineering & Physical Science Research Council
1/06/12 → 30/09/14
Project: Research Councils