International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 153-165

# 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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