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Graphs with few hamiltonian cycles
Mathematics of Computation, 2019 29 pages; to appear in Mathematics of ...
Goedgebeur, Jan +2 more
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Grafos hamiltonianos en el diseño de viajes
Modelling in Science Education and Learning, 2013 The existence and, if applicable, the location of paths with given properties is a topic in graph theory. One of these problems is to find routes through all points, only once, starting and ending at the same node.
Cristina Jordán Lluch +1 more
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Electronic Journal of Graph Theory and Applications, 2021 A Hamiltonian graph G = (V,E) is called hyper-Hamiltonian if G-v is Hamiltonian for any v ∈ V(G). G is called a circulant if its automorphism group contains a |V(G)|-cycle.
Zbigniew R. Bogdanowicz
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Second Hamiltonian Cycles in Claw-Free Graphs
Theory and Applications of Graphs, 2015 Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and ...
Hossein Esfandiari +3 more
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The H-force sets of the graphs satisfying the condition of Ore’s theorem
Open Mathematics, 2020 Let G be a Hamiltonian graph. A nonempty vertex set X⊆V(G)X\subseteq V(G) is called a Hamiltonian cycle enforcing set (in short, an H-force set) of G if every X-cycle of G (i.e., a cycle of G containing all vertices of X) is a Hamiltonian cycle.
Zhang Xinhong, Li Ruijuan
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Tverberg’s Theorem, Disks, and Hamiltonian Cycles [PDF]
Annals of Combinatorics, 2021 8 pages, 3 ...
Pablo Soberón, Yaqian Tang
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Matchings Extend to Hamiltonian Cycles in 5-Cube
Discussiones Mathematicae Graph Theory, 2018 Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture.
Wang Fan, Zhao Weisheng
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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.
Reay, J. R., Zamfirescu, T.
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Hamiltonian cycles and travelling salesfolk
International Journal of Science and Research (IJSR), 2023 A method is given in this paper that makes it easier to solve both the Hamiltonian cycle problem and the travelling salesman problem in any number of space dimensions and in both their directed and undirected varieties.
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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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