The.Algorithm.Design.Manual.Springer-Verlag.1998

Hamiltonian Cycle
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Hamiltonian Cycle
Input description: A graph G = (V,E).
Problem description: Find an ordering of the vertices such that each vertex is visited exactly once.
Discussion: The problem of finding a Hamiltonian cycle or path in a graph is a special case of the
traveling salesman problem, one where each pair of vertices with an edge between them is considered to
have distance 1, while nonedge vertex pairs are separated by distance .
Closely related is the problem of finding the longest path or cycle in a graph, which occasionally arises in
pattern recognition problems. Let the vertices in the graph correspond to possible symbols, and let
edges link symbols that can possibly be next to each other. The longest path through this graph is likely
the correct interpretation.
The problems of finding longest cycles and paths are both NP-complete, even on very restrictive classes
of unweighted graphs. There are several possible lines of attack, however:
● Do you have to visit all the vertices or all the edges? - First verify that you really have a
Hamiltonian cycle problem. As discussed in Section , fast algorithms exist for edge-tour, or
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