## Finding Hamilton Paths and Circuits

On a graph, a *Hamilton's path* is a path that passes through all the vertices of the graph, each vertex exactly once. *Hamilton's path* which is a cycle is called *Hamilton's cycle*. *Circuit* is another term for a *closed* path. Connectivity of the graph is a necessary but not a sufficient condition for the existence of an Hamilton path.

There is no definite prescription for finding Hamilton paths. Start at a node and try your luck. The instructions for using the applet are available on a separate page and can also be read under the first tab directly in the applet.

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(This applet was created to accompany *Excursions in Modern Mathematics*, Seventh Edition, by Peter Tannenbaum © Pearson Education. Reproduced with permission.)

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Copyright © 1996-2018 Alexander Bogomolny69651919