Planar L-Drawings of Directed Graphs
DOI:
https://doi.org/10.57717/cgt.v2i1.43Abstract
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.
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Copyright (c) 2023 Steven Chaplick, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Martin Nöllenburg, Maurizio Patrignani, Ioannis G. Tollis, Alexander Wolff
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