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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, January 3, 2018 - 4:19:10 PM
Last modification on : Wednesday, November 3, 2021 - 7:56:54 AM
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David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, et al.. Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2018, 20 (1), pp.1-11. ⟨10.23638/DMTCS-20-1-1⟩. ⟨hal-01529154v2⟩



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