Published online by Cambridge University Press: 17 April 2009
A graph G on p ≥ 2 vertices is said to be hypotraversable if G is not traversable but G − v is traversable, that is, G − v has an open trail which contains all the vertices and edges of G − v, for each vertex v of G. In this paper we first characterize hypotraversable graphs and then, using this characterization, obtain a complete enumeration of these graphs on p vertices for each positive integer p.