#### Title

### ALGORITHM FOR FINDING HAMILTON CYCLES IN A RANDOM GRAPH.

#### Abstract

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 with n vertices are considered equally likely, then using dynamic programming on failure leads to an algorithm with polynomial expected time. Finally, it is used in an algorithm for solving the symmetric bottleneck travelling salesman problem with probability tending to 1, as n tends to infinity .

#### Publication Title

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

#### Recommended Citation

Bollobas, B., Fenner, T., & Frieze, A.
(1985). ALGORITHM FOR FINDING HAMILTON CYCLES IN A RANDOM GRAPH..* Conference Proceedings of the Annual ACM Symposium on Theory of Computing*, 430-439.
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