Monotone Simultaneous Embeddings of Paths in R^d
Computational Geometry
2016-09-01 v1 Data Structures and Algorithms
Abstract
We study the following problem: Given paths that share the same vertex set, is there a simultaneous geometric embedding of these paths such that each individual drawing is monotone in some direction? We prove that for any dimension , there is a set of paths that does not admit a monotone simultaneous geometric embedding.
Cite
@article{arxiv.1608.08791,
title = {Monotone Simultaneous Embeddings of Paths in R^d},
author = {David Bremner and Olivier Devillers and Marc Glisse and Sylvain Lazard and Giuseppe Liotta and Tamara Mchedlidze and Sue Whitesides and Stephen Wismath},
journal= {arXiv preprint arXiv:1608.08791},
year = {2016}
}