WALCOM 2015: WALCOM: Algorithms and Computation pp 222-233

# Simultaneous Drawing of Planar Graphs with Right-Angle Crossings and Few Bends

• Michael A. Bekos
• Thomas C. van Dijk
• Philipp Kindermann
• Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8973)

## Abstract

Given two planar graphs that are defined on the same set of vertices, a RAC simultaneous drawing is a drawing of the two graphs where each graph is drawn planar, no two edges overlap, and edges of one graph can cross edges of the other graph only at right angles. In the geometric version of the problem, vertices are drawn as points and edges as straight-line segments. It is known, however, that even pairs of very simple classes of planar graphs (such as wheels and matchings) do not always admit a geometric RAC simultaneous drawing.

In order to enlarge the class of graphs that admit RAC simultaneous drawings, we allow edges to have bends. We prove that any pair of planar graphs admits a RAC simultaneous drawing with at most six bends per edge. For more restricted classes of planar graphs (e.g., matchings, paths, cycles, outerplanar graphs, and subhamiltonian graphs), we significantly reduce the required number of bends per edge. All our drawings use quadratic area.

## Keywords

Planar Graph Edge Incident Vertical Segment Horizontal Segment Outerplanar Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Michael A. Bekos
• 1
• Thomas C. van Dijk
• 2
• Philipp Kindermann
• 2
• Alexander Wolff
• 2
1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
2. 2.Lehrstuhl für Informatik IUniversität WürzburgGermany