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GD 2011: Graph Drawing pp 379-390

# Monotone Drawings of Graphs with Fixed Embedding

• Patrizio Angelini
• Walter Didimo
• Stephen Kobourov
• Tamara Mchedlidze
• Vincenzo Roselli
• Antonios Symvonis
• Stephen Wismath
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

## Abstract

A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most 4n – 10 bends in total; such a drawing can be computed in linear time and requires polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2012

## Authors and Affiliations

• Patrizio Angelini
• 1
• Walter Didimo
• 2
• Stephen Kobourov
• 3
• Tamara Mchedlidze
• 4
• Vincenzo Roselli
• 1
• Antonios Symvonis
• 4
• Stephen Wismath
• 5
1. 1.Università Roma TreItaly
2. 2.Università degli Studi di PerugiaItaly
3. 3.University of ArizonaUSA
4. 4.National Technical University of AthensGreece
5. 5.University of LethbridgeCanada