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arXiv · 1104.1307

On Sets of Lines Not-Supporting Trees

Radoslav Fulek·Daniel Neuwirth
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Abstract

We study the following problem introduced by Dujmovic et al. Given a tree $T = (V,E)$, on $n$ vertices, a set of $n$ lines $\mathcal{L}$ in the plane and a bijection $\iota: V \rightarrow \mathcal{L}$, we are asked to find a crossing-free straight-line embedding of $T$ so that $v\in \iota(v)$, for all $v\in V$. We say that a set of $n$ lines $\mathcal{L}$ is universal for trees if for any tree $T$ and any bijection $\iota$ there exists such an embedding. We prove that any sufficiently big set of lines is not universal for trees, which solves an open problem asked by Dujmovic et al.

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Radoslav Fulek, Daniel Neuwirth. 2011-04-07. On Sets of Lines Not-Supporting Trees. https://arxiv.org/abs/1104.1307

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