Bounds for the coefficients of flow polynomials
type: Item
instance of: scholarly article
title: Bounds for the coefficients of flow polynomials
zbMATH Open document ID: 1117.05041
published in: Journal of Combinatorial Theory. Series B
publication date: 2007-04-16T00:00:00Z
review text: Let \(G\) be any connected bridgeless \((n,m)\)-graph which may have loops and multiedges. It is known that the flow polynomial \(F(G,t)\) of \(G\) is a polynomial of degree \(m-n+1\); \(F(G,t)=t-1\) if \(m=n\); and \(F(G,t)\in \{(t-1)^{2},(t-1)(t-2\}\) if \(m=n+1\). It is shown that if \(m\geq n+2\), then the absolute value of the coefficient of \(t^{i}\) in the expansion of \(F(G,t)\) is bounded above by the coefficient of \(t^{i}\) in the expansion of \( (t+1)(t+2)(t+3)(t+4)^{m-n-2}\) for each \(i\) with \(0\leq i\leq m-n+1\).
reviewed by: Giacomo Bonanno
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5143580
zbMATH Keywords: near-cubic graph
zbMATH Keywords: cubic graph
zbMATH Keywords: contraction
zbMATH Keywords: subdivision
author: F. M. Dong
author: K. M. Koh
MaRDI profile type: Publication
full work available at URL: j.jctb.2006.07.005
OpenAlex ID: W2065944804
cites work: Zeros of chromatic and flow polynomials of graphs
cites work: Tension-flow polynomials on graphs
cites work: Decomposition of the flow polynomial
cites work: Nowhere-zero 6-flows
cites work: Q4795883
cites work: A Contribution to the Theory of Chromatic Polynomials
cites work: Q3216652
DOI: 10.1016/J.JCTB.2006.07.005
description: scientific article; zbMATH DE number 5143580