Results 41 to 50 of about 841,975 (192)

The One-Fault Directed Dimension-Balanced Hamiltonian Problem in Directed Toroidal Mesh Graphs

Applied Sciences
Hamiltonian cycle problems play a central role in graph theory and have wide-ranging applications in network-on-chip architectures, interconnection networks, and large-scale parallel systems.
Yancy Yu-Chen Chang, Justie Su-Tzu Juan
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A Survey on Hamiltonian Cycles

Interdisciplinary Information Sciences, 2001
The author surveys some of the classical results on Hamiltonian cycles in undirected graphs and pays particular attention to the development over the last decade. Among the subjects are: binding number, toughness, degree conditions, closure, regular graphs, and graphs on surfaces. This is intended as a supplement to the survey of \textit{R. J.
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Hamiltonian Cycles in the Square of a Graph [PDF]

The Electronic Journal of Combinatorics, 2011
We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a
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Hamiltonian paths on Platonic graphs

International Journal of Mathematics and Mathematical Sciences, 2004
We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate
Brian Hopkins
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A Theorem on Even Pancyclic Bipartite Digraphs

Mathematical Problems of Computer Science, 2021
We prove a Meyniel-type condition and a Bang-Jensen, Gutin and Li-type condition for a strongly connected balanced bipartite digraph to be even pancyclic. Let D be a balanced bipartite digraph of order 2a ≥ 6.
Samvel Kh. Darbinyan
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On vertices enforcing a Hamiltonian cycle

Discussiones Mathematicae Graph Theory, 2013
A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G.
Igor Fabrici, Erhard Hexel, Stanislav Jendrol'   +2 more
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A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
Graph ...
Olga Bodroža-Pantić, Harris Kwong, Milan Pantić   +2 more
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Hamiltonian Dynamics in the Theory of Abstraction [PDF]

, 2012
This paper deals with fluid flow dynamics which may be Hamiltonian in nature and yet chaotic.Here we deal with sympletic invariance, canonical transformations and stability of such Hamiltonian flows. As a collection of points move along, it carries along
Ganguly, Subhajit, Subhajit Ganguly (97729)   +1 more
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Hamiltonian Cycles on Ammann-Beenker Tilings

Physical Review X
We provide a simple algorithm for constructing Hamiltonian graph cycles (visiting every vertex exactly once) on a set of arbitrarily large finite subgraphs of aperiodic two-dimensional Ammann-Beenker (AB) tilings.
Shobhna Singh, Jerome Lloyd, Felix Flicker   +2 more
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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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