Bipartite covering graphs

In this paper we study when a bipartite graph is a covering of a non-bipartite graph. We give a characterization of all coverings in terms of factoring the covering map through the canonical double covering. We also consider regular bipartite coverings described in terms of voltage assignments. We give an algebraic characterization of such coverings involving the subgroup generated by voltages on closed walks of even length. This allows us to count the number of regular bipartite coverings for orders which are twice a prime.