An Orientation Theorem for Graphs

A.M.H. Gerards
1994 Journal of combinatorial theory. Series B (Print)  
We characterize the class of graphs in which the edges can be oriented in such a way that going along any circuit in the graph, the number of forward edges minus the number of backward edges is equal to 0, 1, or -1. The result follows by applying Tutte's characterization of regular matroids to a certain binary matroid associated to a graph. irj
doi:10.1006/jctb.1994.1064 fatcat:u4qp44dwfjcitasfo7fmosyuwi