On a straight-line embedding problem of graphs

On a straight-line embedding problem of forests

Computing straight skeletons of planar straight-line graphs based on motorcycle graphs

We present a simple algorithm for computing straight skeletons of planar straight-line graphs. We exploit the relation between motorcycle graphs and straight skeletons, and introduce a wavefront-propagation algorithm that circumvents the expensive search for the next split event. Our algorithm maintains the simplicity of the triangulation-based algorithm by Aichholzer and Aurenhammer but has a ...

Straight Line Representations of Infinite Planar Graphs

graphs are denoted by capital roman letters and plane graphs by capital greek letters. If the graph G is isomorphic to the plane graph F, then F is a representation of G. If the edges of F are polygonal arcs (respectively straight line segments), then F is a polygonal arc representation (respectively straight line representation). A closed Jordan curve partitions the Euclidean plane into a boun...

Straight-line Drawings of 1-planar Graphs

The classical Fáry’s theorem from the 1930s states that every planar graph can be drawn as a straight-line drawing. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-planar graphs with straight-line edges. A 1-planar graph is a sparse non-planar graph with at most one crossing per edge. We give a characterisation of those 1planar ...

Straight-Line Rectangular Drawings of Clustered Graphs

We show that every c-planar clustered graph has a straight-line c-planar drawing in which each cluster is represented by an axis-parallel rectangle, thus solving a problem posed by Eades, Feng, Lin, and Nagamochi [Algorithmica, 2006 ].