Monotone Simultaneous Embeddings of Paths in d Dimensions

Bremner, David and Devillers, Olivier and Glisse, Marc and Lazard, Sylvain and Liotta, Giuseppe and Mchedlidze, Tamara and Whitesides, Sue and Wismath, Stephen (2016) Monotone Simultaneous Embeddings of Paths in d Dimensions. In: Graph Drawing and Network Visualization. GD 2016, September, 19. - 21., 2016 , pp. 546-553(Official URL:

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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, there is a set of d+1 paths that does not admit a monotone simultaneous geometric embedding.

Item Type: Conference Paper
Classifications: G Algorithms and Complexity > G.490 Embeddings
G Algorithms and Complexity > G.560 Geometry
P Styles > P.999 Others

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