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In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
A verifier algorithm for Hamiltonian path will take as input a graph G, starting vertex s, and ending vertex t. Additionally, verifiers require a potential solution known as a certificate, c. For the Hamiltonian Path problem, c would consist of a string of vertices where the first vertex is the start of the proposed path and the last is the end ...
(Hamilton originally thought in terms of moves between the faces of an icosahedron, which is equivalent by duality. This is the origin of the name "icosian". [3]) Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. [4]
Illustration for the proof of Ore's theorem. In a graph with the Hamiltonian path v 1...v n but no Hamiltonian cycle, at most one of the two edges v 1 v i and v i − 1 v n (shown as blue dashed curves) can exist. For, if they both exist, then adding them to the path and removing the (red) edge v i − 1 v i would produce a Hamiltonian cycle.
This is intended to be a complete list of the properties and districts on the National Register of Historic Places in Newton County, Arkansas, United States. The locations of National Register properties and districts for which the latitude and longitude coordinates are included below, may be seen in a map. [1]
The U.S. Highways in Arkansas are the U.S. Routes maintained by the U.S. state of Arkansas. There are 20 such highways. There are 20 such highways. 1926 map of the U.S. Highways in Arkansas
Arkansas Highway 7 (AR 7) is a north–south state highway in Arkansas. As Arkansas's longest state highway, the route runs 297.27 miles (478.41 km) from the Louisiana state line north to Diamond City .
The Arkansas Scenic Byways Program is a list of highways, mainly state highways, that have been designated by the Arkansas Department of Transportation (ArDOT) as scenic highways. The Arkansas General Assembly designates routes for scenic byway status upon successful nomination. For a highway to be declared scenic, a group interested in ...