A Characterization of Biplanar Graphs
Shunichi Toida · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · 1969
Abstract : A graph is called biplanar if it can be permitted into two planar graphs. For example planar graphs are biplanar. Relations between biplanar graphs and degree of their vertices are sought. The following are main results: If every vertex in a graph has degree less than 5, then the graph is biplanar. If every vertex in a graph has degree greater than 11 then the graph is not biplanar. There is a graph regular of degree 7 which is not biplanar, but we do not know whether graphs regular of degree 5 or 6 are biplanar or not. There is no known method of constructing non-biplanar graphs. One way of doing that from a given nonbiplanar graph is presented. (Author)