论文信息 - Monotone Simultaneous Embeddings of Paths in d Dimensions

Monotone Simultaneous Embeddings of Paths in d Dimensions

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.

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