DeepAI
Log In Sign Up

Towards a characterization of stretchable aligned graphs

08/14/2020
by   Marcel Radermacher, et al.
0

We consider the problem of stretching pseudolines in a planar straight-line drawing to straight lines while preserving the straightness and the combinatorial embedding of the drawing. We answer open questions by Mchedlidze et al. by showing that not all instances with two pseudolines are stretchable. On the positive side, for k≥ 2 pseudolines intersecting in a single point, we prove that in case that some edge-pseudoline intersection-patterns are forbidden, all instances are stretchable. For intersection-free pseudoline arrangements we show that every aligned graph has an aligned drawing. This considerably reduces the gap between stretchable and non-stretchable instances.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/29/2017

Aligned Drawings of Planar Graphs

Let G be a graph topological embedded in the plane and let A be an arra...
04/14/2019

Drawing HV-Restricted Planar Graphs

A strict orthogonal drawing of a graph G=(V, E) in R^2 is a drawing of G...
08/31/2017

On the Edge-length Ratio of Outerplanar Graphs

We show that any outerplanar graph admits a planar straightline drawing ...
11/02/2018

Drawing Clustered Graphs on Disk Arrangements

Let G=(V, E) be a planar graph and let C be a partition of V. We refer t...
07/31/2019

Level-Planar Drawings with Few Slopes

We introduce and study level-planar straight-line drawings with a fixed ...
11/25/2008

String Art: Circle Drawing Using Straight Lines

An algorithm to generate the locus of a circle using the intersection po...
01/24/2019

Infinite All-Layers Simple Foldability

We study the problem of deciding whether a crease pattern can be folded ...