Monotone Simultaneous Embeddings of Paths in R^d

August 31, 2016 Β· Declared Dead Β· πŸ› Discrete Mathematics & Theoretical Computer Science

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Authors David Bremner, Olivier Devillers, Marc Glisse, Sylvain Lazard, Giuseppe Liotta, Tamara Mchedlidze, Sue Whitesides, Stephen Wismath arXiv ID 1608.08791 Category cs.CG: Computational Geometry Cross-listed cs.DS Citations 0 Venue Discrete Mathematics & Theoretical Computer Science Last Checked 3 months ago
Abstract
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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