Kathrin Hanauer

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A graph is outer 1-planar (o1p) if it can be drawn in the plane such that all vertices are in the outer face and each edge is crossed at most once. o1p graphs generalize outerplanar graphs, which can be recognized in linear time, and specialize 1-planar graphs, whose recognition is $${NP}$$ N P -hard. We explore o1p graphs. Our first main result is a(More)
A graph is outer 1-planar (o1p) if it can be drawn in the plane such that all vertices are on the outer face and each edge is crossed at most once. o1p graphs generalize outerplanar graphs, which can be recognized in linear time and specialize 1-planar graphs, whose recognition is NP-hard. Our main result is a linear-time algorithm that first tests whether(More)
A graph is NIC-planar if it admits a drawing in the plane with at most one crossing per edge and such that two pairs of crossing edges share at most one common end vertex. NIC-planarity generalizes IC-planarity, which allows a vertex to be incident to at most one crossing edge, and specializes 1-planarity, which only requires at most one crossing per edge.(More)
The feedback arc set problem plays a prominent role in the four-phase framework to draw directed graphs, also known as the Sugiyama algorithm. It is equivalent to the linear arrangement problem where the vertices of a graph are ordered from left to right and the backward arcs form the feedback arc set. In this paper we extend classical sorting algorithms to(More)
We consider directed planar graphs with an upward planar drawing on the rolling and standing cylinders. These classes extend the upward planar graphs in the plane. Here, we address the dual graphs. Our main result is a combinatorial characterization of these sets of upward planar graphs. It basically shows that the roles of the standing and the rolling(More)
A graph is upward planar if it can be drawn without edge crossings such that all edges point upward. Upward planar graphs have been studied on the plane, the standing and rolling cylinders. For all these surfaces, the respective decision problem NP-hard in general. Efficient algorithms exist if the graph contains a single source and a single sink, but only(More)
We consider upward planar drawings of directed graphs in the plane (UP), and on standing (SUP) and rolling cylinders (RUP). In the plane and on the standing cylinder the edge curves are monotonically increasing in y-direction. On the rolling cylinder they wind unidirectionally around the cylinder. There is a strict hierarchy of classes of upward planar(More)