A new characterization of planar graphs
Charles H. C. Little, Derek Holton · Bulletin of the American Mathematical Society · 1977
We consider graphs on a finite set of vertices.In addition the graphs are undirected, although, for the purposes of the characterization, we will need to give each edge a direction.We use the notation EG to denote the set of edges of the graph G, and VG for the corresponding vertex set.A graph is defined to be planar if and only if it can be embedded in the plane so that any two edges intersect at a common end-vertex or not at all.Our characterization of planar graphs is given by the following theorem.For other characterizations, see [1].