Decomposing complete 3-uniform hypergraph kn(3) into 7-cycles

• Autorzy: Meihua , Guan Meiling , Jirimutu

Identyfikatory

DOI

10.7494/OpMath.2019.39.3.383

• Języki publikacji: EN

Abstrakty

EN

We use the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph. A decomposition of complete k-uniform hypergraph [formula] into Hamiltonian cycles was studied by Bailey-Stevens and Meszka-Rosa. For n ≡ 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 [formula] into 5-cycles has been presented for all admissible n ≤ 17, and for all n = 4m + 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 [formula] sequences (ki0, ki1,…..,k16) on Dall(n), then [formula] can be decomposed into 7-cycles. We use the method of edge-partition and cycle sequence. We find a decomposition of [formula] and [formula] into 7-cycles.

Słowa kluczowe

EN

uniform hypergraph; 7-cycle; cycle decomposition

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 3
• Strony: 383--–393
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Meihua

• Mongolia University for the Nationalities College of Mathematics of Inner Tongliao, China 028043

autor

Guan Meiling

• Mongolia University for the Nationalities College of Mathematics of Inner Tongliao, China 028043

autor

Jirimutu

• Mongolia University for the Nationalities College of Mathematics of Inner Tongliao, China 028043

Bibliografia

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