@Article{Meihua2019,
author = "Meihua and Guan, Meiling and Jirimutu",
title = "Decomposing complete 3-uniform hypergraph K<sub>n</sub><sup>(3)</sup> into 7-cycles",
journal = "Opuscula Math.",
year = "2019",
volume = "39",
number = "3",
pages = "383--393",
doi = "https://doi.org/10.7494/OpMath.2019.39.3.383",
url = "https://doi.org/10.7494/OpMath.2019.39.3.383",
abstract = "We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete \(k\)-uniform hypergraph \(K^{(k)}_{n}\) into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For \(n\equiv 2,4,5\pmod 6\), we design an algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of \(K^{(3)}_{n}\) into 5-cycles has been presented for all admissible \(n\leq17\), and for all \(n=4^{m}+1\) when \(m\) is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we show if \(42~|~(n-1)(n-2)\) and if there exist \(\lambda=\frac{(n-1)(n-2)}{42}\) sequences \((k_{i_{0}},k_{i_{1}},\ldots,k_{i_{6}})\) on \(D_{all}(n)\), then \(K^{(3)}_{n}\) can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of \(K^{(3)}_{37}\) and \(K^{(3)}_{43}\) into 7-cycles.",
keywords = "uniform hypergraph, 7-cycle, cycle decomposition",
issn = "1232-9274"
}