On a theorem about vertex colorings of graphs
type: Item
instance of: scholarly article
title: On a theorem about vertex colorings of graphs
zbMATH Open document ID: 0625.05021
DOI: 10.1016/0012-365X(87)90243-3
author: Claudio Bernardi
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A nice and short proof is given of the following Theorem: ``Let G be a finite graph. Let \(f_ 0,f_ 1,...,f_ n\) be real-valued functions on V(G) such that for every vertex v, \(\sum_{i}f_ i(v)>d(v)\) (the degree of v). Then there exists a colouring c: V(G)\(\to \{0,1,...,n\}\) such that every vertex v is adjacent to fewer than \(f_{c(v)}(v)\) vertices with the same colour as v'', which is due to \textit{J. Lawrence} [Discr. Math. 21, 61-68 (1978; Zbl 0371.05024)] and \textit{O. V. Borodin} and \textit{A. V. Kostochka} [J. Comb. Theory, Ser. B 23, 247-250 (1977; Zbl 0336.05104)].
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 4014749
zbMATH Keywords: vertex-colouring
reviewed by: H. P. Yap
MaRDI profile type: Publication
cites work: On an upper bound of the graph's chromatic number, depending on the graph's degree and density
cites work: Covering the vertex set of a graph with subgraphs of smaller degree
full work available at URL: 0012-365x(87)90243-3
OpenAlex ID: W1979074854
description: scientific article; zbMATH DE number 4014749