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.
@article{arxiv.1601.01598,
title = {Strongly Monotone Drawings of Planar Graphs},
author = {Stefan Felsner and Alexander Igamberdiev and Philipp Kindermann and Boris Klemz and Tamara Mchedlidze and Manfred Scheucher},
journal= {arXiv preprint arXiv:1601.01598},
year = {2016}
}