Geodesic
Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1

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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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     author = {Bremner, David and Devillers, Olivier and Glisse, Marc and Lazard, Sylvain and Liotta, Giuseppe and Mchedlidze, Tamara and Moroz, Guillaume and Whitesides, Sue and Wismath, Stephen},
     title = {Monotone {Simultaneous} {Paths} {Embeddings} in $\mathbb{R}^d$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2018},
     doi = {10.23638/DMTCS-20-1-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-1/}
}
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%A Glisse, Marc
%A Lazard, Sylvain
%A Liotta, Giuseppe
%A Mchedlidze, Tamara
%A Moroz, Guillaume
%A Whitesides, Sue
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%J Discrete mathematics & theoretical computer science
%D 2018
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%N 1
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Bremner, David; Devillers, Olivier; Glisse, Marc; Lazard, Sylvain; Liotta, Giuseppe; Mchedlidze, Tamara; Moroz, Guillaume; Whitesides, Sue; Wismath, Stephen. Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi: 10.23638/DMTCS-20-1-1

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