Planar L-drawings of directed graphs

Abstract

In this paper, we study drawings of directed graphs. We use the L-drawing standard where each edge is represented by a polygonal chain that consists of a vertical line segment incident to the source of the edge and a horizontal line segment incident to the target. First, we consider planar L-drawings. We provide necessary conditions for the existence of these drawings and show that testing for the existence of a planar L-drawing is an NP-complete problem. We also show how to decide in linear time whether there exists a planar L-drawing of a plane directed graph with a fixed assignment of the edges to the four sides (top, bottom, left, and right) of the vertices. Second, we consider upward- (resp. upward-rightward-) planar L-drawings. We provide upper bounds on the maximum number of edges of graphs admitting such drawings. Moreover, we characterize the directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing as exactly those admitting an embedding supporting a bitonic (resp. monotonically decreasing) st-ordering.