Hamilton path problem

The purpose of this survey of classical mechanics is twofold first, to indicate the path whereby the more general formulations of classical dynamics, such as the equations of motion of Lagrange and of Hamilton, have been developed from the original equations of Newton and second, to illustrate the application of these methods to problems which are later discussed by quantum-mechanical methods. 

Storage, though, is all very well, but how can the information be written and retrieved An exploratory experiment, based, to be sure, on laborious biochemistry, was performed by L. M. Adleman more than a decade ago. As a first demonstration of the watery DNA computer in action he chose to solve a simple form of what mathematicians know as the Hamiltonian path, or travelling salesman problem—how, starting from city A, to travel to each of a succession of other cities, terminating at city Z, without ever retracing your path. A formal solution to this ancient mathematical teaser was worked out in the early nineteenth century by two mathematicians. Sir William Rowan Hamilton in Ireland and Thomas Kirkman in England. With their aid an answer can be easily found if the number of cities is small, but if there are many it requires an enormous amount of computer time. 

In the middle of the 19th century, the famous four color problem , originating with Francis Guthrie29° (1790—1868), appeared and has continued to challenge mathematicians for over 150 years. Another challenging problem in which a path is sought that visits every vertex of a graph was put forth by W. R. Hamilton.290 932,933 difficult problem, also known... 

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