Strong Connectivity of Polyhedral Complexes

A classical theorem of Robbins states that the edges of a graph may be oriented, in such a way that an oriented path exists between any source and destination, if and only if the graph is both connected and twoconnected (it cannot be disconnected by the removal of an edge). In this paper, an algebraic version of Robbins' result becomes a lemma on Hilbert bases for free abelian groups, which is then applied to generalize his theorem to higher dimensional complexes. An application to cycle bases for graphs is given, and various examples are presented.