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arXiv · 1601.01598

Strongly Monotone Drawings of Planar Graphs

Stefan Felsner·Alexander Igamberdiev·Philipp Kindermann·Boris Klemz·Tamara Mchedlidze·Manfred Scheucher
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Abstract

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs are based on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.

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Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, Manfred Scheucher. 2016-01-07. Strongly Monotone Drawings of Planar Graphs. https://arxiv.org/abs/1601.01598

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