English

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 kk 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 d2d \geq 2, there is a set of d+1d+1 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}
}
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