Recursive characterization of maximal bipartite planar graphs

In this paper, we initiate our study by demonstrating that bipartite-minors, derived through vertex/edge deletions and edge contractions within a bond, inherently preserve the bipartite property. Leveraging this, we establish a well-quasi-ordering on the class of bipartite graphs. Subsequently, we provide elegant and succinct characterizations of bipartite graphs, planar bipartite graphs, and outer-planar bipartite graphs, all formulated in terms of excluded bipartite-minors. Finally, we introduce a novel planar operation that enables the recursive construction of all maximal bipartite planar graphs, starting from a single vertex.