关于非支撑树的线集
On Sets of Lines Not-Supporting Trees
摘要：
我们研究了Dujmovic等人提出的以下问题。给定一棵树$T = (V,E)$，在$n$顶点上，一组$n$线$\mathcal{L}$在平面上和一个双射$ι: V \rightarrow \mathcal{L}$，我们被要求找到一个无交叉的直线嵌入$T$，使$v\in ι(v)$，对于所有$v\in V$。我们说一组$n$线$\mathcal{L}$对树是通用的，如果对任何树$T$和任何双射$ι$存在这样的嵌入。我们证明，任何足够大的线集是不普遍的树，解决了一个开放的问题Dujmovic等。
英文摘要：
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 $ι: V \rightarrow \mathcal{L}$, we are asked to find a crossing-free straight-line embedding of $T$ so that $v\in ι(v)$, 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 $ι$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
