Generalizations of planar graphs
Ranel E. Erickson · Networks · 1982
Abstract Two new generalizations of planar graphs, called quasiplanar and pseudoplanar graphs, are introduced and discussed. It is shown that planar graphs are quasiplanar and these in turn are pseudoplanar. Conversely, a pseudoplanar graph that contains with each arc its reverse arc is quasiplanar. A Kuratowski‐type characterization of quasiplanar graphs is given; in it the excluded subgraphs differ from Kuratowski's only by the addition of an edge in the bipartite graph.