On the complexity of the maximum biplanar subgraph problem

Abstract

A typical convention for drawing G is to put the vertices of S on a line and the vertices of T on a separate parallel line and then represent edges by placing straight line segments between the vertices that determine them . In this convention, a drawing is biplanar if it has a biplanar drawing.The maximum biplanar subgraph problem is to find a biplanar subgraph with a maximum number of edges. In general, this maximum biplanar subgraph problem is NP-complete, In this paper, we show the Maximum biplanar subgraph problem belongs to not only the class P, but also the class NC, when input graphs are restricted to doubly convex-bipartite graphs. Moreover, our sequential algorithm is optimal.