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

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...

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Vydané v:	Discrete mathematics and theoretical computer science Ročník 20 no. 1; číslo Discrete Algorithms; s. 1 - 11
Hlavní autori:	Bremner, David, Devillers, Olivier, Glisse, Marc, Lazard, Sylvain, Liotta, Giuseppe, Mchedlidze, Tamara, Moroz, Guillaume, Whitesides, Sue, Wismath, Stephen
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	DMTCS 05.01.2018 Discrete Mathematics & Theoretical Computer Science
Predmet:	[info.info-cg] computer science [cs]/computational geometry [cs.cg] algorithm Computational Geometry Computer Science graph drawing high-dimensional space point hyperplane duality graph drawing point hyperplane duality algorithm high-dimensional space
ISSN:	1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí:	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.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.23638/DMTCS-20-1-1