On graph planarity and semi-duality Original Research Article

In this (partly expository) paper we describe some of our recent results on graph planarity. These results concern strengthenings of Kuratowskiʹs planarity criterion for quasi-4-connected graphs, for bipartite quasi-4-connected graphs, and for cubic bipartite graphs as well as generalizations of matroid duality of graphs and strengthenings of Whitneyʹs planarity criterion.