A note on chain lengths and the Tutte polynomial
type: Item
instance of: scholarly article
title: A note on chain lengths and the Tutte polynomial
zbMATH Open document ID: 1161.05036
author: Ronald C. Read
author: Earl Glen jun. Whitehead
published in: Discrete Mathematics
publication date: 2008-11-12T00:00:00Z
review text: Replace an edge in a graph \(G\) by a set of edges in series, that is, by a path. This operation is also known as a sequence of subdivisions. The resulting graph is homeomorphic to \(G\). The authors show that the number of chains of a given length can be easily found by the Tutte polynomial. Hence two Tutte-equivalent graphs will have the same distribution of chain lengths. They give two applications of this statement. They also give dual results for the number of multiple edges given their multiplicity.
reviewed by: Dan S. Archdeacon
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5365245
zbMATH Keywords: Tutte polynomial
zbMATH Keywords: homeomorphism
MaRDI profile type: Publication
full work available at URL: j.disc.2006.09.049
OpenAlex ID: W2055976471
cites work: Q3313882
cites work: Q3786495
cites work: Chromatic polynomials of homeomorphism classes of graphs
cites work: The Tutte polynomial for homeomorphism classes of graphs
DOI: 10.1016/J.DISC.2006.09.049
description: scientific article; zbMATH DE number 5365245