An algorithm for finding hamilton paths and cycles in random graphs


This paper describes a polynomial time algorithm HAM that searches for Hamilton cycles in undirected graphs. On a random graph its asymptotic probability of success is that of the existence of such a cycle. If all graphs withn vertices are considered equally likely, then using dynamic programming on failure leads to an algorithm with polynomial expected time. The algorithm HAM is also used to solve the symmetric bottleneck travelling salesman problem with probability tending to 1, asn tends to ∞.

Various modifications of HAM are shown to solve several Hamilton path problems.

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Supported by NSF Grant MCS 810 4854.

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Bollobás, B., Fenner, T.I. & Frieze, A.M. An algorithm for finding hamilton paths and cycles in random graphs. Combinatorica 7, 327–341 (1987).

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AMS subject classification

  • 05 C 45
  • 68 E 10