PACKINGS AND PERFECT PATH DOUBLE COVERS OF MAXIMAL PLANAR GRAPHS

A maximal planar graph is a simple planar graph in which every face is a triangle, and a perfect packing of such a graph by 2-cliques and fa cial triangles corresponds to a partition of the vertex set into class es, each of which induces either a 2-clique or a facial triangle in th e graph. We prove a sufficient condition for a maximal planar graph to have a perfect packing by 2-cliques and facial triangles. This result then leads to a construction of a special type of perfect path double cover of a maximal planar graph.