Results 41 to 50 of about 3,095,070 (339)
On Hamiltonian alternating cycles and paths
Computational Geometry, 2018 We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same ...
Claverol Aguas, Mercè +4 more
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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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Cycles of many lengths in Hamiltonian graphs [PDF]
Forum of Mathematics, Sigma, 2021 Abstract In 1999, Jacobson and Lehel conjectured that, for $k \geq 3$ , every k-regular Hamiltonian graph has cycles of $\Theta (n)$ many different lengths. This was further strengthened by Verstraëte, who asked whether the regularity can be replaced with the weaker condition that the ...
Matija Bucić +2 more
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Proper Hamiltonian Cycles in Edge-Colored Multigraphs [PDF]
, 2017 A $c$-edge-colored multigraph has each edge colored with one of the $c$ available colors and no two parallel edges have the same color. A proper Hamiltonian cycle is a cycle containing all the vertices of the multigraph such that no two adjacent edges ...
Borozan, Valentin +4 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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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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Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian [PDF]
, 2015 This note shows there are infinitely many finite groups G, such that every connected Cayley graph on G has a hamiltonian cycle, and G is not solvable. Specifically, for every prime p that is congruent to 1, modulo 30, we show there is a hamiltonian cycle
Morris, Dave Witte
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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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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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Hamiltonian Cycles in T-Graphs [PDF]
Discrete & Computational Geometry, 2000 There is only one finite, 2-connected, linearly convex graph in the Archimedean triangular tiling that does not have a Hamiltonian cycle.
Tudor Zamfirescu, John R. Reay
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