Direction trees
type: Item
instance of: scholarly article
title: Direction trees
zbMATH Open document ID: 0615.05026
DOI: 10.1007/BF02187882
author: Robert E. Jamison
published in: Discrete \& Computational Geometry
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131021
review text: A direction tree for a finite set X of points in the plane is a tree T whose vertices are the points of X such that any two edges of T determine lines with different slopes. Ungar's theorem says that any n noncollinear points in the real affine plane determine at least different n-1 slopes among connecting lines. This note uses Ungar's theorem plus Hall's theorem on distinct representatives to prove the existence of a direction tree for any finite set of noncollinear points.
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 3995709
zbMATH Keywords: direction tree
zbMATH Keywords: Ungar's theorem
zbMATH Keywords: Hall's theorem
zbMATH Keywords: noncollinear points
reviewed by: Alan C. Tucker
MaRDI profile type: Publication
cites work: Q3958473
cites work: On Representatives of Subsets
cites work: Q3326356
cites work: Q4727753
cites work: On the Sets of Directions Determined by n Points
cites work: 2N noncollinear points determine at least 2N directions
OpenAlex ID: W2912623622
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description: scientific article; zbMATH DE number 3995709