Bipartite minors

Maria Chudnovsky, Gil Kalai, Eran Nevo, Isabella Novik, Paul Seymour
2016 Journal of combinatorial theory. Series B (Print)  
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 K 3,3 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)-Laman graphs -a certain family of graphs that contains all maximal bipartite planar graphs.
doi:10.1016/j.jctb.2015.08.001 fatcat:buoguul2tfc7np4lyy5fyxzzce