3 research outputs found
Planar L-Drawings of Directed Graphs
We study planar drawings of directed graphs in the L-drawing standard. 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.
Motivated by this result, we focus on upward-planar L-drawings. We show that
directed st-graphs admitting an upward- (resp. upward-rightward-) planar
L-drawing are exactly those admitting a bitonic (resp. monotonically
increasing) st-ordering. We give a linear-time algorithm that computes a
bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or
reports that there exists none.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Planar L-Drawings of Bimodal Graphs
In a planar L-drawing of a directed graph (digraph) each edge e is
represented as a polyline composed of a vertical segment starting at the tail
of e and a horizontal segment ending at the head of e. Distinct edges may
overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs
admitting a planar embedding in which the incoming and outgoing edges around
each vertex are contiguous. We show that every plane bimodal graph without
2-cycles admits a planar L-drawing. This includes the class of upward-plane
graphs. Finally, outerplanar digraphs admit a planar L-drawing - although they
do not always have a bimodal embedding - but not necessarily with an
outerplanar embedding.Comment: Appears in the Proceedings of the 28th International Symposium on
Graph Drawing and Network Visualization (GD 2020
New Approaches to Classic Graph-Embedding Problems - Orthogonal Drawings & Constrained Planarity
Drawings of graphs are often used to represent a given data set in a human-readable way. In this thesis, we consider different classic algorithmic problems that arise when automatically generating graph drawings. More specifically, we solve some open problems in the context of orthogonal drawings and advance the current state of research on the problems clustered planarity and simultaneous planarity