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Conference Papers Year : 2016

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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Dates and versions

hal-01366148 , version 1 (14-09-2016)

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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. ⟨10.1007/978-3-319-50106-2_42⟩. ⟨hal-01366148⟩
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