A note on caterpillar-embeddings with no two parallel edges
type: Item
instance of: scholarly article
title: A note on caterpillar-embeddings with no two parallel edges
zbMATH Open document ID: 1072.52018
author: Daniel J. Kleitman
author: Rom Pinchasi
published in: Discrete \& Computational Geometry
publication date: 2005-04-15T00:00:00Z
review text: The authors prove in their paper the following: Let \(C\) be any given caterpillar on \(n\) vertices, and let \(G\) be any set of \(n\) points in general position in the plane. Then there is a rectilinear embedding of \(C\) in the plane so that the vertices of \(C\) are the points of \(G\) and every pair of edges of \(C\) have different directions. In fact, they prove a slightly stronger result. Their result proves a conjecture of Robert E. Jamison. As an open problem the authors ask if the result of their paper remains true if \(C\) is any tree on \(n\) vertices. If the set of points \(G\) is the set of vertices of a regular \(n\)-gon this problem is equivalent to the so-called Harmonic Tree Conjecture.
reviewed by: S. Nickel
Mathematics Subject Classification ID: 52C30
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 2156868
zbMATH Keywords: caterpillar
zbMATH Keywords: embedding
MaRDI profile type: Publication
full work available at URL: s00454-004-1142-2
OpenAlex ID: W2075374312
DOI: 10.1007/S00454-004-1142-2
description: scientific article; zbMATH DE number 2156868