Bipartite minors

We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain K3,3K3,3 as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite (2,2)(2,2)-Laman graphs — a certain family of graphs that contains all maximal bipartite planar graphs.