Spanning maximal planar subgraphs of random graphs

Abstract: "We study the threshold for the existence of a spanning maximal planar subgraph in the random graph G[subscript n,p]. We show that it is very near p = 1[over][subscript n]1/3. We also discuss the threshold for the existence of a spanning maximal outerplanar subgraph. This is very near p = 1[over][subscript n]1/2."