Hamilton Circuits in Graphs and Directed Graphs
  We give polynomial-time algorithms for obtaining hamilton circuits in random graphs, G, and random directed graphs, D. If n is finite, we assume that G or D contains a hamilton circuit. If G is an arbitrary graph containing a hamilton circuit, we conjecture that Algorithm G always obtains a hamilton circuit in polynomial time. 
Howard Kleiman (Prof. Emer., Queensborough Community Coll. (CUNY))