Hamiltonian decomposition of complete bipartiter-hypergraphs

Jirimutu,; Wang, Jianfang

doi:10.1007/bf02669710

Cited by 13 publications

(12 citation statements)

References 3 publications

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“…(1, 4), (1,5), (1,6), (1,7), (1,8), (1,9), (1,10), (1,11), (1,12), (1,13), (1,14), (1,15), (1,16), (1,17), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8), (2,9), (2,10), (2,11), (2,12), (2,13), (2,14), (2,15), (2,…”

Section: Theorem 31 a Necessary Condition For The Decomposition Of mentioning

confidence: 99%

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Decomposing complete 3-uniform hypergraph K_{n}^{(3)} into 7-cycles

Meihua¹,

Meiling²,

Jirimutu³

2019

Opuscula Math.

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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.

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Section: Theorem 31 a Necessary Condition For The Decomposition Of mentioning

confidence: 99%

“…In fact, the two different definitions of a Hamiltonian cycle are the same. A decomposition of complete k-uniform hypergraphs into Hamiltonian cycles has been considered in [1,3,4,6,10,[13][14][15]. In the paper [10], Hamiltonian decompositions of K (3) n for all admissible n ≤ 32 has been resolved.…”

Section: Introductionmentioning

confidence: 99%

Decomposing complete 3-uniform hypergraph K_{n}^{(3)} into 7-cycles

Meihua¹,

Meiling²,

Jirimutu³

2019

Opuscula Math.

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“…In fact, two different definitions of Hamiltonian chain and Hamiltonian cycle are the same. Some researchers studied the decomposition of complete 3-uniform hypergraph   3 n K into Hamiltonian cycles and not Hamiltonian cycles in [2][3][4][5][6][7][8][9]. Especially , Bailey Stevens [3] used clique-finding the decomposition of   3 n K into Hamiltonian cycles for   3 7 K ,   3 8 K and Meszka-Rosa [4] showed that Hamiltonian decompositions of …”

Section: Introductionmentioning

confidence: 99%

Decomposing Complete 3-uniform Hypergraph into 7-cycles

Meiling¹,

Xu²

2017

Advances in Computer Science Research

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“…Jirimutu and J. Wang gave the following definition of bipartite k-uniform hypergraphs in [10] and then provided a Berge Hamilton cycle decomposition of their complete bipartite 3-uniform hypergraph for prime orders.…”

Section: Introductionmentioning

confidence: 99%