scholarly journals Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs

2020 ◽  
Vol 161 (2) ◽  
pp. 647-699
Author(s):  
J. Polcyn ◽  
Chr. Reiher ◽  
V. Rödl ◽  
A. Ruciński ◽  
M. Schacht ◽  
...  
Keyword(s):  
Hamiltonian Cycles ◽  
Degree Condition ◽  
Uniform Hypergraphs

scholarly journals Minimum vertex degree condition for tight Hamiltonian cycles in 3‐uniform hypergraphs

2019 ◽  
Vol 119 (2) ◽  
pp. 409-439 ◽  
Author(s):  
Christian Reiher ◽  
Vojtěch Rödl ◽  
Andrzej Ruciński ◽  
Mathias Schacht ◽  
Endre Szemerédi
Keyword(s):  
Vertex Degree ◽  
Hamiltonian Cycles ◽  
Degree Condition ◽  
Uniform Hypergraphs

Decomposing Complete 3-Uniform Hypergraph into 5-Cycles

2014 ◽  
Vol 672-674 ◽  
pp. 1935-1939
Author(s):  
Guan Ru Li ◽  
Yi Ming Lei ◽  
Jirimutu
Keyword(s):  
Positive Integer ◽  
Hamiltonian Cycles ◽  
Uniform Hypergraph ◽  
Design Algorithm ◽  
Uniform Hypergraphs ◽  
Edge Partition ◽  
Definition Of

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=4m +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.

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

2019 ◽  
Vol 39 (3) ◽  
pp. 383-393
Author(s):  
Meihua Meihua ◽  
Meiling Guan ◽  
Jirimutu Jirimutu
Keyword(s):  
Positive Integer ◽  
Hamiltonian Cycle ◽  
Hamiltonian Cycles ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Edge Partition ◽  
Definition Of

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.

Hamiltonian decompositions of prisms over complete 3-uniform hypergraphs

2015 ◽  
Vol 07 (03) ◽  
pp. 1550031
Author(s):  
Ratinan Boonklurb ◽  
Sirirat Singhun ◽  
Sansanee Termtanasombat
Keyword(s):  
Hamiltonian Cycles ◽  
Uniform Hypergraphs ◽  
Hamiltonian Decompositions

We consider prisms over complete 3-uniform hypergraphs and decompose them into Hamiltonian cycles of Katona–Kierstead type. We show that prisms over complete 3-uniform hypergraphs of order 4, 5 and 8 can be decomposed into Hamiltonian cycles and we suggest that prisms over complete 3-uniform hypergraphs of order in the form 6t + 2 may have Hamiltonian decompositions.

scholarly journals Squares of Hamiltonian cycles in 3‐uniform hypergraphs

2019 ◽  
Vol 56 (2) ◽  
pp. 339-372 ◽  
Author(s):  
Wiebke Bedenknecht ◽  
Christian Reiher
Keyword(s):  
Hamiltonian Cycles ◽  
Uniform Hypergraphs

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

scholarly journals Rainbow matchings for 3-uniform hypergraphs

2021 ◽  
Vol 183 ◽  
pp. 105489
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Uniform Hypergraphs
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