A Characterization of Weakly Bipartite Graphs

A signed graph is said to be weakly bipartite if the clutter of its odd circuits is ideal. P. D. Seymour (1977, J. Combin. Theory Ser. B23, 189–122; 1981, Europ. J. Combin. 257–290) conjectured that a signed graph is weakly bipartite if and only if it does not contain a minor called an odd K5. A proof of this conjecture is given in this paper.