Results 11 to 20 of about 311 (214)
Hamiltonian Cycles in Cayley Graphs of Gyrogroups
Mathematics, 2022 In this study, we investigate Hamiltonian cycles in the right-Cayley graphs of gyrogroups. More specifically, we give a gyrogroup version of the factor group lemma and show that some right-Cayley graphs of certain gyrogroups are Hamiltonian.
Rasimate Maungchang +3 more
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Decomposing complete 3-uniform hypergraph K_{n}^{(3)} into 7-cycles [PDF]
Opuscula Mathematica, 2019 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 \(n\equiv 2,4,5\pmod 6\)
Meihua, Meiling Guan, Jirimutu
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Hamiltonian cycles on bicolored random planar maps
Nuclear Physics B, 2023 We study the statistics of Hamiltonian cycles on various families of bicolored random planar maps (with the spherical topology). These families fall into two groups corresponding to two distinct universality classes with respective central charges c=−1 ...
Bertrand Duplantier +2 more
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Hamiltonian Chains in Hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Hamiltionian chain is a generalisation of hamiltonian cycles for hypergraphs. Among the several possible ways of generalisations this is probably the most strong one, it requires the strongest structure.
Gyula Y. Katona
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Finding hidden hamiltonian cycles [PDF]
Random Structures & Algorithms, 1991 AbstractConsider a random graph G composed of a Hamiltonian cycle on n labeled vertices and dn random edges that “high” the cycle. Is it possible to unravel the structures, that is, to efficiently find a Himiltonian cycle in G? We describe an O(n3 log n)‐step algorithm A for this purpose, and prove that it succeeds almost surely. Part one of A properly
Andrei Z. Broder +2 more
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Enumerating Hamiltonian Cycles [PDF]
The Electronic Journal of Combinatorics, 2014 A dynamic programming method for enumerating hamiltonian cycles in arbitrary graphs is presented. The method is applied to grid graphs, king's graphs, triangular grids, and three-dimensional grid graphs, and results are obtained for larger cases than previously published.
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The Traveling Salesman Problem for Cubic Graphs
Journal of Graph Algorithms and Applications, 2007 We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2n/3) ≈ 1.260n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound.
David Eppstein
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Hamiltonian Cycles in T-Graphs [PDF]
Discrete & Computational Geometry, 2000 The vertices and polygonal edges of the planar Archimedean tiling \(3^6\) of the plane is called the triangular tiling graph (TTG). A subgraph \(G\) of TTG is linearly convex if, for every line \(L\) which contains an edge of TTG, the set \(L \cap G\) is a (possibly degenerated or empty) line segment.
John R. Reay, Tudor Zamfirescu
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Enforced hamiltonian cycles in generalized dodecahedra
Electronic Journal of Graph Theory and Applications, 2013 The H-force number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with |W| = k such that each cycle passing through all vertices of W is a hamiltonian cycle.
Maria Timkova
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On Hamiltonian Cycles in Claw-Free Cubic Graphs
Discussiones Mathematicae Graph Theory, 2022 We show that every claw-free cubic graph of order n at least 8 has at most 2⌊n4⌋{2^{\left\lfloor {{n \over 4}} \right\rfloor }} Hamiltonian cycles, and we also characterize all extremal graphs.
Mohr Elena, Rautenbach Dieter
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