it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

It has been proved that sphericity testing for digraphs is an NP-complete problem. Here, we investigate sphericity of 3-connected single source digraphs. We provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. Our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $O(n)$ time.

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph D has an upward planar embedding into a point set S. We show that any switch tree admits an upward planar straight-line embedding into any convex point set. For the class of k-switch trees, that is a generalization of switch trees (according to this definition a switch t...

This paper studies the problem of computing an upward topological book embedding of an upward planar digraph G, i.e. a topological book embedding of G where all edges are monotonically increasing in the upward direction. Besides having its own inherent interest in the theory of upward book embeddability, the question has applications to well studied research topics of computational geometry and...

In this paper we consider the problem of characterizing the directed graphs that admit an upward straight-line embedding into every point set in convex or in general position. In particular, we show that no biconnected directed graph admits an upward straight-line embedding into every point set in convex position, and we provide a characterization of the Hamiltonian directed graphs that admit u...

We consider planar upward drawings of directed graphs on arbitrary surfaces where the upward direction is defined by a vector field. This generalizes earlier approaches using surfaces with a fixed embedding in R and introduces new classes of planar upward drawable graphs, where some of them even allow cycles. Our approach leads to a classification of planar upward embeddability. In particular, ...

We study the problem of characterizing the directed graphs with an upward straightline embedding into every point set in general or in convex position. We solve two questions posed by Binucci et al. [Computational Geometry: Theory and Applications, 2010 ]. Namely, we prove that the classes of directed graphs with an upward straightline embedding into every point set in convex position and with ...

An upward embedding of an embedded planar graph states, for ea h vertex v, whi h edges are in ident to v \above" or \below" and, in turn, indu es an upward orientation of the edges. In this paper we hara terize the set of all upward embeddings and orientations of a plane graph by using a simple ow model. We take advantage of su h a ow model to ompute upward orientations with the minimum number ...

Let G be a directed acyclic graph. An upward (k, h)topological book embedding of G is an upward book embedding on k pages of a subdivision of G where every edge is replaced by a path having at most h+2 vertices. In this extended abstract it is shown that every DAG with n vertices admits an upward (d + 1, 2dlogd ne − 1)-topological book embedding, where d is any integer such that d ≥ 2. The resu...

The upward planarity testing problem is known to be NPhard. We describe an O(n)-time upward planarity testing and embedding algorithm for the class of digraphs that do not contain rigid triconnected components. We also present a new FPT algorithm that solves the upward planarity testing and embedding problem for general digraphs.