Carla Binucci

Fan-planarity

In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. Fan-planar drawings have been recently introduced by Kaufmann and Ueckerdt 35], who proved that every n-vertex fan-planar drawing has at most 5 n - 10 edges, and that this bound is tight for n ? 20 . We extend their result from both the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the relationship between fan-planarity and k-planarity. Also, we prove that testing fan-planarity in the variable embedding setting is NP-complete.In a \emph{fan-planar drawing} of a graph an edge can cross only edges with a common end-vertex. Fan-planar drawings have been recently introduced by Kaufmann and Ueckerdt, who proved that every

Upward straight-line embeddings of directed graphs into point sets

n

Orthogonal drawings of graphs with vertex and edge labels

-vertex fan-planar drawing has at most

Drawing trees in a streaming model

5n-10

Maximum upward planar subgraphs of embedded planar digraphs

edges, and that this bound is tight for

Upward planarity testing of embedded mixed graphs

n \geq 20

Upward and quasi-upward planarity testing of embedded mixed graphs

. We extend their result, both from the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the relationship between fan-planarity and

Switch-Regular Upward Planarity Testing of Directed Trees

k

Labeling Heuristics for Orthogonal Drawings

-planarity. Furthermore, we prove that deciding whether a graph admits a fan-planar drawing in the variable embedding setting is NP-complete.

Fan-Planar Graphs: Combinatorial Properties and Complexity Results

In this paper we study the problem of computing an upward straight-line embedding of a planar DAG (directed acyclic graph) G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented according to a common direction. In particular, we show that no biconnected DAG admits an upward straight-line embedding into every point set in convex position. We provide a characterization of the family of DAGs that admit an upward straight-line embedding into every convex point set such that the points with the largest and the smallest y-coordinate are consecutive in the convex hull of the point set. We characterize the family of DAGs that contain a Hamiltonian directed path and that admit an upward straight-line embedding into every point set in general position. We also prove that a DAG whose underlying graph is a tree does not always have an upward straight-line embedding into a point set in convex position and we describe how to construct such an embedding for a DAG whose underlying graph is a path. Finally, we give results about the embeddability of some sub-classes of DAGs whose underlying graphs are trees on point set in convex and in general position.