Bremner, David; Devillers, Olivier; Glisse, Marc; Lazard, Sylvain; Liotta, Giuseppe; Mchedlidze, Tamara; Moroz, Guillaume; Whitesides, Sue; Wismath, Stephen Monotone simultaneous paths embeddings in \(\mathbb{R}^d\). (English) Zbl 1401.05198 Discrete Math. Theor. Comput. Sci. 20, No. 1, Paper No. 1, 11 p. (2018). 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. MSC: 05C62 Graph representations (geometric and intersection representations, etc.) 05C38 Paths and cycles 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:graph drawing; point hyperplane duality; high-dimensional space PDFBibTeX XMLCite \textit{D. Bremner} et al., Discrete Math. Theor. Comput. Sci. 20, No. 1, Paper No. 1, 11 p. (2018; Zbl 1401.05198) Full Text: Link