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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2018

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

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David Bremner
• Function : Author
• PersonId : 988936
Olivier Devillers
Marc Glisse
Sylvain Lazard
Giuseppe Liotta
• Function : Author
Tamara Mchedlidze
• Function : Author
Guillaume Moroz
Sue Whitesides
• Function : Author
Stephen Wismath
• Function : Author

#### 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.

### Dates and versions

hal-01529154 , version 1 (30-05-2017)
hal-01529154 , version 2 (03-01-2018)

### Identifiers

• HAL Id : hal-01529154 , version 2
• DOI :

### Cite

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, 2018, Vol. 20 no. 1 (1), pp.1-11. ⟨10.23638/DMTCS-20-1-1⟩. ⟨hal-01529154v2⟩

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