On Beck's coloring of posets
type: Item
instance of: scholarly article
title: On Beck's coloring of posets
zbMATH Open document ID: 1190.06001
author: Radomír Halaš
author: Marek Jukl
published in: Discrete Mathematics
publication date: 2009-12-10T00:00:00Z
review text: The authors study Beck-like coloring of partially ordered sets with a least element 0. To any poset \(P\) with \(0\) they assign a graph, called a zero-divisor graph, whose vertices are labelled by the elements of \(P\) with two vertices \(x,y\) adjacent if \(0\) is the only element lying below \(x\) and \(y\). They prove that for such graphs the chromatic number and the clique number coincide. Further, they give a condition under which posets are not finitely colorable. The main result of the paper is similar to Dilworth's theorem.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 5644978
zbMATH Keywords: coloring of a poset
zbMATH Keywords: clique number
zbMATH Keywords: chromatic number
zbMATH Keywords: annihilator
zbMATH Keywords: order ideal
MaRDI profile type: Publication
full work available at URL: j.disc.2009.02.024
OpenAlex ID: W2067162317
cites work: The zero-divisor graph of a commutative ring
cites work: Beck's coloring of a commutative ring
cites work: Coloring of commutative rings
cites work: Distributive laws for concept lattices
cites work: Properties of rings with a finite number of zero divisors
cites work: Q3568727
cites work: A course in combinatorics.
DOI: 10.1016/J.DISC.2009.02.024
description: scientific article; zbMATH DE number 5644978