Small-Area Orthogonal Drawings of 3-Connected Graphs

TL;DR

This paper presents a new method for creating small-area orthogonal drawings of 3-connected graphs, reducing the area bounds significantly using a novel application of Mondshein sequences.

Contribution

It introduces the first application of Mondshein sequences in graph drawing to achieve smaller area bounds for 3-connected graphs.

Findings

Area reduced to approximately 0.56n^2 for 3-connected graphs.

Uses 3-canonical order and Mondshein sequence for linear-time computation.

First known application of Mondshein sequence in graph drawing.

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.