×

Monotone simultaneous paths embeddings in \(\mathbb{R}^d\). (English) Zbl 1401.05198

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
PDFBibTeX XMLCite
Full Text: Link