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arXiv · 1608.08791

Monotone Simultaneous Embeddings of Paths in R^d

David Bremner·Olivier Devillers·Marc Glisse·Sylvain Lazard·Giuseppe Liotta·Tamara Mchedlidze·Sue Whitesides·Stephen Wismath
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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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David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, Tamara Mchedlidze, Sue Whitesides, Stephen Wismath. 2016-08-31. Monotone Simultaneous Embeddings of Paths in R^d. https://arxiv.org/abs/1608.08791

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