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Abstract
In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if n divides (nk), then the complete kuniform 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 KruskalKatona theorem. The case when k = 3 was already solved by Verrall, building on results of Bermond.
Original language  English 

Pages (fromto)  128135 
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

EdgeColourings and Hamilton Decompostitions of Graphs
Engineering & Physical Science Research Council
1/06/12 → 30/09/14
Project: Research Councils