On orienting graphs for connectivity: Projective planes and Halin graphs

Nash-Williams proved that the edges of a k-edge connected (undirected) graph can be oriented such that the resulting directed graph is left perpendiculark/2right perpendicular-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity, element connectivity, and hypergraph edge connectivity. We focus on two special classes of graphs, namely, incidence graphs of projective planes and (generalized) Halin graphs, and we prove some analogs of Nash-Williams' result for these classes. (C) 2012 Elsevier B.V. All rights reserved.