Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$

Abstract : We study the following problem: Given $k$ 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 $d\geq 2$, there is a set of $d + 1$ paths that does not admit a monotone simultaneous geometric embedding.
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Submitted on : Wednesday, September 14, 2016 - 10:37:17 AM
Last modification on : Friday, September 20, 2019 - 4:56:35 PM

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  • HAL Id : hal-01366148, version 1
  • ARXIV : 1608.08791

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David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, et al.. Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$. 24th International Symposium on Graph Drawing & Network Visualization, Sep 2016, Athens, Greece. ⟨hal-01366148⟩

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