- Tytuł:
- Decomposing complete 3-uniform hypergraph $K_n^{(3)}$ into 7-cycles
- Autorzy:
-
Meihua, -
Guan, Meiling
Jirimutu, - - Powiązania:
- https://bibliotekanauki.pl/articles/1397516.pdf
- Data publikacji:
- 2019
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
uniform hypergraph
7-cycle
cycle decomposition - Opis:
- We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete k-uniform hypergraph $K_n^{(k)}$ into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For $ n \equiv 2,4, 5 (mod 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_n^{(3)}$ into 5-cycles has been presented for all admissible $ n \leq 17$, 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 $\lambda = (n-1)(n-2)/42$ sequences $(k_{i0}, k_{i1},…..,k_{i6})$ on $D_{\text{all}}(n)$, then $K_n^{(3)}$ can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of $K_{37}^{(3)}$ and $K_{43}^{(3)}$ into 7-cycles.
- Źródło:
-
Opuscula Mathematica; 2019, 39, 3; 383-393
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł