TY  - JOUR
ID  - Meihua2019
LB  - Meihua2019
AU  - Meihua
AU  - Guan, Meiling
AU  - Jirimutu
TI  - Decomposing complete 3-uniform hypergraph K<sub>n</sub><sup>(3)</sup> into 7-cycles
ST  - Decomposing complete 3-uniform hypergraph K<sub>n</sub><sup>(3)</sup> into 7-cycles
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 3
SP  - 383
EP  - 393
DO  - https://doi.org/10.7494/OpMath.2019.39.3.383
UR  - https://doi.org/10.7494/OpMath.2019.39.3.383
AB  - 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.
KW  - uniform hypergraph
KW  - 7-cycle
KW  - cycle decomposition
SN  - 1232-9274
ER  -