  This version is similar to math.CO/0210113. We've changed Conjectures 1.1 and
1.2 so that they cover arbitrary graphs(digraphs). Let G be an arbitrary
graph(digraph). Then - in polynomial time - either an algorithm obtains a
hamilton circuit(cycle)or else the algorithm points to at least one vertex that
cannot belong to any hamilton circuit(cycle) of G. We give criteria for
determining which vertices should be examined.

Combinatorics