An orientation theorem for graphs
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.
scientific article; zbMATH DE number 696907