GD 2014: Graph Drawing pp 40-51

# Drawing Simultaneously Embedded Graphs with Few Bends

• Luca Grilli
• Seok-Hee Hong
• Jan Kratochvíl
• Ignaz Rutter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

## Abstract

We study the problem of drawing simultaneously embedded graphs with few bends. We show that for any simultaneous embedding with fixed edges (Sefe) of two graphs, there exists a corresponding drawing realizing this embedding such that common edges are drawn as straight-line segments and each exclusive edge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (Sge) for a non-trivial class of graphs.

## Keywords

Planar Graph Input Graph Outer Face Internal Edge Embed 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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## Authors and Affiliations

• Luca Grilli
• 1
• Seok-Hee Hong
• 2
• Jan Kratochvíl
• 3
• Ignaz Rutter
• 3
• 4
1. 1.Dipartimento di IngegneriaUniversità degli Studi di PerugiaItaly
2. 2.School of Information TechnologiesUniversity of SydneyAustralia
3. 3.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles University in PragueCzech Republic
4. 4.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany