Bipartite and Eulerian minors

This paper defines the related notions of bipartite and Eulerian minors for binary matroids. Using these definitions, it characterizes graphic matroids within the classes of bipartite binary matroids and Eulerian binary matroids by the exclusion of certain bipartite minors and Eulerian minors, respectively. This result on Eulerian minors in binary matroids extends a result of Chudnovsky et al. who characterized planar graphs within the class of bipartite graphs by the exclusion of K3,3 as a bipartite minor.