On the cone of nonnegative circuits (Q1080435)

In this paper, three equivalent formulations of a theorem of \textit{P. D. Seymour} [Sums of circuits, Graph Theory and Related Topics, Proc. Conf. Honour W. T. Tutte, Waterloo/Ont. 1977, 341-355 (1979; Zbl 0465.05042)] on nonnegative sums of circuits of a graph are discussed and proved. Also, the authors prove a stronger result of which one of the equivalent formulation of Seymour's result is a corollary. This fact yields a different, but not shorter proof of the remarkable theorem of Seymour.