2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65212This 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.PDF file, 71 pages. In this version, we change Conjectures 1.1 and 1.2 so that an algorithm either obtains a hamilton circuit(cycle), or else it points to at least one vertex that cannot belong to any graph(digraph). We give criteria for determining which vertices should be examinedCombinatorics05text