An extension of König's theorem to graphs with no odd-K4

Mathematics

Signed graphs, regular matroids, grafts

Mathematics

A short proof of Tutte's characterization of totally unimodular matrices

AbstractWe give, in terms of totally unimodular matrices, a short and easy proof of Tutte's characterization of regular matroids

An Orientation Theorem for Graphs

AbstractWe 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