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## Hamiltonian path

Line graphs may have other Hamiltonian cycles that do not correspond to Euler tours, and in particular the line graph L G of every Hamiltonian graph Canino is itself Hamiltonian, regardless of whether the graph G is Eulerian. An email notifying of the reuse would be appreciated but not required.

You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. I, the copyright holder of this work, hereby publish it under the following license:. This article is about the nature of Hamiltonian paths.

Spanish graph theory glossary. Retrieved from ” acmino In the mathematical field of graph theorya Hamiltonian path or traceable path is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycleHamiltonian circuitvertex tour or graph cycle is a cycle that visits each vertex exactly once except for the vertex that is both the start and end, which is visited twice. A Hamilton maze is a type of logic puzzle in which the goal is to find the unique Hamiltonian cycle in a given graph.

By using this site, you agree to hamiltoniani Terms of Use and Camono Policy. Different usage terms may also be discussed via email. This file hamiltonizno additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it.

All Hamiltonian graphs are biconnectedbut a biconnected graph need not be Hamiltonian see, for example, the Petersen graph. Any Hamiltonian cycle can be converted to a Hamiltonian path by removing one of its edges, but a Hamiltonian path can be extended to Hamiltonian cycle only if its endpoints hamiltoinano adjacent.

Hamiltonianno imagen se ha publicado bajo una licencia Creative Commonscomo se detalla debajo. Fonts and Preparing images for upload: This implies that you’re freely allowed to reuse and make derived works from this image provided section 4c of license: These counts assume that cycles that are the same apart from their starting point are not counted separately.

The following hamiptoniano wikis use this file: You properly credit my authorship: Unless rendering the text of the SVG file produces an image with text that is incurably unreadable due to technical limitationsit is highly recommended to revert the text from path.

Interlanguage link template link number. This page was last edited on 29 Septemberat Retrieved 27 May By using this site, you agree to the Terms of Use and Privacy Policy. This page was last edited on 3 Julyat A Hamiltonian decomposition is an edge decomposition of a graph into Hamiltonian circuits.

Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the icosian gamenow also hamilltoniano as Hamilton’s puzzlewhich involves finding a Hamiltonian cycle in the edge graph of the dodecahedron. Hamiltonicity has been widely studied with relation to various parameters such as graph densitytoughnessforbidden subgraphs and distance among other parameters.

### Camino/Ciclo Hamiltoniano by Rafael Calvo on Prezi

Despite hamiiltoniano named after Hamilton, Hamiltonian cycles in polyhedra had also been studied a year earlier by Thomas Kirkmanwho, in particular, gave an example of a polyhedron without Hamiltonian cycles. As complete graphs are Hamiltonian, all graphs whose closure is complete are Hamiltonian, which is namiltoniano content of the following earlier theorems by Dirac and Ore.

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Description Grafo – camino hamiltoniano. Hamilton Mazes – The Beginner’s Guide.

In other projects Wikimedia Commons. A graph that contains a Hamiltonian path is called a traceable graph.

For the question of the existence of a Hamiltonian path or cycle in a given graph, see Hamiltonian path problem. A Hamiltonian path or traceable path is a path that visits each vertex of the graph exactly once. One possible Hamiltonian cycle through every vertex of a dodecahedron is shown in red — like all platonic solidsthe dodecahedron is Hamiltonian.

Hamilton solved this problem using the icosian calculusan algebraic structure based on roots of unity with many similarities to the quaternions also invented by Hamilton.

Knight’s Tours”, Across the Board: Barnette’s conjecturean open problem on Hamiltonicity of cubic bipartite polyhedral graphs Eulerian patha path through all edges in a graph Fleischner’s theoremon Hamiltonian squares of graphs Grinberg’s theorem giving a necessary condition for planar graphs to have a Hamiltonian cycle Hamiltonian path problemthe computational problem of finding Hamiltonian paths Hypohamiltonian grapha non-Hamiltonian graph in which every vertex-deleted subgraph is Hamiltonian Knight’s toura Hamiltonian cycle in the knight’s graph LCF notation for Hamiltonian cubic graphs.

### Hamiltonian path – Wikidata

This solution does not generalize to arbitrary graphs. Similar notions may be defined for directed graphswhere each edge arc of a path or cycle can only be traced in a single direction i. From Wikipedia, the free encyclopedia. For more information, see SVG: A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices.