International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 153-165 | Cite as

Small-Area Orthogonal Drawings of 3-Connected Graphs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

It is well-known that every graph with maximum degree 4 has an orthogonal drawing with area at most \(\frac{49}{64}n^2+O(n)\approx 0.76n^2\). In this paper, we show that if the graph is 3-connected, then the area can be reduced even further to \(\frac{9}{16}n^2+O(n) \approx 0.56n^2\). The drawing uses the 3-canonical order for (not necessarily planar) 3-connected graphs, which is a special Mondshein sequence and can hence be computed in linear time. To our knowledge, this is the first application of a Mondshein sequence in graph drawing.

Notes

Acknowledgments

We wish to thank the anonymous reviewers for their constructive comments.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Institute of MathematicsTU IlmenauIlmenauGermany

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