Another characterisation of Pfaffian bipartite graphs
Charles H. C. Little · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1985
Abstract It has been known for over twenty years that every planar graph is Pfaffian. Recently a characterisation of planar graphs in terms of strict maximal odd rings has been discovered. This paper attempts to elucidate the connection between the Pfaffian property and planarity by characterising Pfaffian bipartite graphs in terms of maximal odd rings.