On Contact Representations Of Directed Planar Graphs

Prior work on contact representations of planar graphs deals with undirected graphs only. We introduce a notion of point-side contact representations for directed planar graphs. We show every outerplanar digraph of out-degree at most three to enjoy a point-side triangle contact representation. The result is generalized to outerplanar digraphs of out-degree at most n, which are shown to have convex n-gon (i.e., n-sided polygon) point-side contact representations. Our result is tight is the sense that there exists a 2-outerplanar digraph that does not have a point-side triangle contact representation. For maximal outerplanar digraphs of out-degree at most three, an efficient constructive procedure is designed to yield their point-side triangle contact representations. For general planar digraphs of degree d, they are shown to admit 2d-gon point-side contact representations.