Monotone Simultaneous Paths Embeddings in $\mathbb{R}^d$
oleh: David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, Tamara Mchedlidze, Guillaume Moroz, Sue Whitesides, Stephen Wismath
| Format: | Article |
|---|---|
| Diterbitkan: | Discrete Mathematics & Theoretical Computer Science 2018-01-01 |
Deskripsi
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.