The Utility of Untangling

TL;DR

This paper demonstrates how existing untangling techniques for planar graphs can be applied to derive new results in graph drawing models, solving some open problems in the field.

Contribution

It introduces novel applications of untangling methods to various graph drawing models, addressing previously open questions.

Findings

New results on column planarity and universal point subsets.

Solutions to open problems in partial simultaneous geometric embeddings.

Enhanced understanding of graph drawing models through untangling techniques.

Abstract

In this note we show how techniques developed for untangling planar graphs by Bose et al. [Discrete & Computational Geometry 42(4): 570-585 (2009)] and Goaoc et al. [Discrete & Com- putational Geometry 42(4): 542-569 (2009)] imply new results about some recent graph drawing models. These include column planarity, universal point subsets, and partial simultaneous geometric embeddings (with or without mappings). Some of these results answer open problems posed in previous papers.