Decomposing Complete 3-Uniform Hypergraph into 5-Cycles

Guan Ru Li; Yi Ming Lei; Jirimutu Jirimutu

doi:10.4028/www.scientific.net/AMM.672-674.1935

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 672-674Decomposing Complete 3-Uniform Hypergraph into...

Decomposing Complete 3-Uniform Hypergraph into 5-Cycles

Abstract:

About the Katona-Kierstead definition of a Hamiltonian cycles in a uniform hypergraph, a decomposition of complete k-uniform hypergraph Kn^(k) into Hamiltonian cycles studied by Bailey-Stevens and Meszka-Rosa. For n≡2,4,5 (mod 6), we design algorithm for decomposing the complete 3-uniform hypergraphs into Hamiltonian cycles by using the method of edge-partition. A decomposition of Kn⁽³⁾ into 5-cycles has been presented for all admissible n≤17, and for all n=4^m +1, m is a positive integer. In general, the existence of a decomposition into 5-cycles remains open. In this paper, we use the method of edge-partition and cycle sequence proposed by Jirimutu and Wang. We find a decomposition of K20⁽³⁾ into 5-cycles.

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Periodical:

Applied Mechanics and Materials (Volumes 672-674)

Pages:

1935-1939

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.672-674.1935

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Online since:

October 2014

Authors:

Guan Ru Li, Yi Ming Lei, Jirimutu Jirimutu

Keywords:

5-cycle, Cycle Decomposition, Uniform Hypergraph

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