Reduced 2-to-1 maps and decompositions of graphs with no 2-to-1 cut sets
type: Item
instance of: scholarly article
title: Reduced 2-to-1 maps and decompositions of graphs with no 2-to-1 cut sets
zbMATH Open document ID: 1025.54009
DOI: 10.1016/S0166-8641(01)00217-6
author: Van Nall
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: \textit{J. Heath} [Continua with the Houston problem book, Lect. Notes Pure Appl. Math. 170, 89-102, Marcel Dekker, N.Y. (1995; Zbl 0852.54013)] has asked: given an integer \(k> 0\) and two graphs \(G\) and \(H\), when does there exist a \(k\)-to-\(1\) (continuous) map from \(G\) onto \(H\)? Here, a graph is a continuum which is a finite union of arcs with a finite number of points having order greater than two. The author has previously shown that a graph is the image of a tree under a \(2\)-to-\(1\) map with no \(2\)-to-\(1\) restriction to a continuum iff the graph satisfies a graph connectivity condition (``\(k\)-to-\(1\) cut set''). In this paper the author characterizes such graphs in terms of a graph decomposition property (``increasing ear decomposition'').
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 1879071
zbMATH Keywords: \(k\)-to-\(1\) map
zbMATH Keywords: \(k\)-to-\(1\) cut set
reviewed by: Louis M. Friedler
MaRDI profile type: Publication
cites work: Reduced \(k\)-to-1 maps and graphs with no \(k\)-to-1 cut set
cites work: Q3880849
cites work: Ear-decompositions of matching-covered graphs
cites work: Q4871750
full work available at URL: s0166-8641(01)00217-6
OpenAlex ID: W2038492183
description: scientific article; zbMATH DE number 1879071