Hamilton decompositions of complete 3-uniform hypergraphs

Verrall, H.

doi:10.1016/0012-365x(92)00572-9

Cited by 31 publications

(28 citation statements)

References 2 publications

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“…In order to decompose

K_{n}^{h}

into Hamiltonian cycles, it is clearly necessary that

n false| (\frac{0pt}{n})

. The results of Bermond , Verrall , Kühn and Osthus collectively imply that this condition is sufficient as long as n is not too small.…”

Section: Introductionmentioning

confidence: 99%

Partitioning the edge set of a hypergraph into almost regular cycles

Bahmanian

Haghshenas

2018

J of Combinatorial Designs

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A cycle of length t in a hypergraph is an alternating sequence v1,e1,v2⋯,vt,et of distinct vertices vi and distinct edges ei so that false{vi,vi+1false}⊆ei (with vt+1:=v1). Let λKnh be the λ‐fold n‐vertex complete h‐graph. Let G=(V,E) be a hypergraph all of whose edges are of size at least h, and 2≤c1≤⋯≤ck≤false|Vfalse|. In order to partition the edge set of scriptG into cycles of specified lengths c1,⋯,ck, an obvious necessary condition is that 0true∑i=1kci=|E|. We show that this condition is sufficient in the following cases. (R1)h≥max{ck,false⌈n/2false⌉+1}. (R2)G=λKnh, h≥⌈n/2⌉+2. (R3)G=Knh, c1=⋯=ck:=c, c|n(n−1),n≥85.In (R2), we guarantee that each cycle is almost regular. In (R3), we also solve the case where a “small” subset L of edges of Knh is removed.

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“…In order to decompose

K_{n}^{h}

into Hamiltonian cycles, it is clearly necessary that

n false| (\frac{0pt}{n})

. The results of Bermond , Verrall , Kühn and Osthus collectively imply that this condition is sufficient as long as n is not too small.…”

Section: Introductionmentioning

confidence: 99%

Partitioning the edge set of a hypergraph into almost regular cycles

Bahmanian

Haghshenas

2018

J of Combinatorial Designs

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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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“…The study of decompositions of complete 3-uniform hypergraphs into cycles of this type was begun by Bermond et al in the 1970s [3] and was completed by Verrall in 1994 [6]. …”

Section: Introductionmentioning

confidence: 99%