Back to Search
Start Over
Decomposition of complete uniform multi‐hypergraphs into Berge paths and cycles.
- Source :
-
Journal of Graph Theory . Jul2018, Vol. 88 Issue 3, p507-520. 14p. - Publication Year :
- 2018
-
Abstract
- Abstract: In 2015, Bryant, Horsley, Maenhaut, and Smith, generalizing a well‐known conjecture by Alspach, obtained the necessary and sufficient conditions for the decomposition of the complete multigraph λ K n − I into cycles of arbitrary lengths, where <italic>I</italic> is empty, when λ ( n − 1 ) is even and <italic>I</italic> is a perfect matching, when λ ( n − 1 ) is odd. Moreover, Bryant in 2010, verifying a conjecture by Tarsi, proved that the obvious necessary conditions for packing pairwise edge‐disjoint paths of arbitrary lengths in λ K n are also sufficient. In this article, first, we obtain the necessary and sufficient conditions for packing edge‐disjoint cycles of arbitrary lengths in λ K n − I. Then, applying this result, we investigate the analogous problem of the decomposition of the complete uniform multihypergraph μ K n ( k ) into Berge cycles and paths of arbitrary given lengths. In particular, we show that for every integer μ ≥ 1, n ≥ 108 and 3 ≤ k < n, μ K n ( k ) can be decomposed into Berge cycles and paths of arbitrary lengths, provided that the obvious necessary conditions hold, thereby generalizing a result by Kühn and Osthus on the decomposition of K n ( k ) into Hamilton Berge cycles. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03649024
- Volume :
- 88
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- 129612190
- Full Text :
- https://doi.org/10.1002/jgt.22226