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A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
The Nauru graph [1] has LCF notation [5, –9, 7, –7, 9, –5] 4.. In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle.
At about the same time as Hamilton, Thomas Kirkman in England was also studying Hamiltonian cycles on polyhedra. [17] Hamilton visited Kirkman in 1861, and presented him with a copy of the icosian game. [10] Despite this related work, some of which was much earlier, Hamiltonian cycles came to be named for Hamilton and for his work on the ...
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A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time.
A graph that can be proven non-Hamiltonian using Grinberg's theorem. In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengths of its face cycles. If a graph does not meet this condition, it is not Hamiltonian.
Astronomy – Axial precession – CNO cycle – Eclipse cycle – Eclipse – Full moon cycle – Galactic year – Great Year – Lunar phase – Mesoamerican calendars – Metonic cycle – Milankovitch cycles – Mira – Moon – Nutation – Orbit – Orbital period – Saros cycle – Sothic cycle – Secularity – Sidereal year ...
A 2-vertex-connected graph, its square, and a Hamiltonian cycle in the square. In graph theory, a branch of mathematics, Fleischner's theorem gives a sufficient condition for a graph to contain a Hamiltonian cycle. It states that, if is a 2-vertex-connected graph, then the square of is Hamiltonian.
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