A bipartite ear decomposition of a bipartite graph is a construction starting with one graph edge and successively adjoining paths of odd length whose endpoints are distinct existing vertices and whose internal vertices are new. Each added graph path is called an ear. A connected bipartite graph in which every graph edge belongs to a perfect matching admits such a decomposition (Lovász and Plummer 1986; Li 2026, pp. 2-3).
For a plane graph, the decomposition is plane when its first graph cycle bounds an interior graph face, and every later ear lies in the exterior of the current partial graph and, together with part of its boundary, bounds an interior graph face of the final graph. A connected plane graph that is bipartite, has at least four vertices, and has every graph edge in a perfect matching is det-extremal iff it has a plane bipartite ear decomposition whose interior graph faces all have boundary length congruent to 2 modulo 4 (Li 2026, pp. 2, 6).
