On Sets of Lines Not-Supporting Trees

Details On Sets of Lines Not-Supporting Trees On Sets of Lines Not-Supporting Trees

2011-04-07

arxiv.org/abs/1104.1307v5

Computer Science

Discrete Mathematics

a revised version

Scientific paper

In this note we study the following problem introduced by Dujmovic et al. Given a tree T = (V,E), on n vertices, a set of n lines L in the plane and a bijection l: V -> L, we are asked to find a straight-line embedding of T so that v in l(v), for all v in V. We say that a set of n lines L is universal for trees if for any tree T and any bijection l there exists such an embedding. We prove that any sufficiently big set of concurrent lines (also called pencil or pinwheel) is not universal for trees, which solves an open problem asked by Dujmovic et al.

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