Two chromatic polynomial conjectures
type: Item
instance of: scholarly article
title: Two chromatic polynomial conjectures
zbMATH Open document ID: 0883.05057
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-10-20T00:00:00Z
review text: Let \(P(t)\) be the chromatic polynomial of a graph. It is shown that \(P(5)^{-1}P(6)^2 P(7)^{-1}\) can be arbitrarily small, disproving a conjecture of Welsh that \(P(t)^2\geq P(t- 1)P(t+1)\), and also disproving several other conjectures of Brenti. Secondly, it is proved that if the graph has \(n\) vertices, then \(P(n)P(n- 1)^{-1}\geq 2.718253\), approaching a conjecture of Welsh and Brenti that \(P(n)P(n-1)^{-1}\geq e\).
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1076878
zbMATH Keywords: chromatic polynomial
zbMATH Keywords: conjecture of Welsh
zbMATH Keywords: conjectures of Brenti
author: Paul Seymour
reviewed by: Chris Jagger
MaRDI profile type: Publication
full work available at URL: jctb.1997.1749
OpenAlex ID: W2020333521
cites work: The Markov chain of colourings
cites work: Expansions of Chromatic Polynomials and Log-Concavity
cites work: An introduction to chromatic polynomials
cites work: Q4111952
DOI: 10.1006/JCTB.1997.1749
description: scientific article; zbMATH DE number 1076878