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arXiv · 1510.02322

Small-Area Orthogonal Drawings of 3-Connected Graphs

Therese Biedl·Jens M. Schmidt
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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.

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Therese Biedl, Jens M. Schmidt. 2015-10-12. Small-Area Orthogonal Drawings of 3-Connected Graphs. https://arxiv.org/abs/1510.02322

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