A SUCCESSFUL ALGORITHM FOR THE UNDIRECTED HAMILTONIAN PATH PROBLEM

A polynomial algorithm called the Minram algorithm is presented which fins a Hamiltonian Path in an undirected graph with high frequency of success for graphs up to 1000 nodes. It is shown that a Hamiltonian Path is a spanning arborescence with zero ramification index. Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence. By suitable pivots it locates a locally minimal value of the ramification index. If this local minima corresponds to zero ramification index then the algorithm is considered to have ended successfully, else a failure is reported. Computational performance of the algorithm on randomly generated Hamiltonian graphs is given.