Entire chromatic number and \(\Delta\)-matching of outerplane graphs
type: Item
instance of: scholarly article
title: Entire chromatic number and \(\Delta\)-matching of outerplane graphs
zbMATH Open document ID: 1083.05019
DOI: 10.1016/S0252-9602(17)30207-2
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2006-02-21T00:00:00Z
review text: A plane graph \(G\) is \(k\)-entire colorable if the elements of \(V(G)\cup E(G)\cup F(G)\) can be colored with \(k\) colors such that any two adjacent or incident elements receive different colors. The entire chromatic number \(\chi_{\text{vef}}(G)\) of \(G\) is the minimum number \(k\) such that \(G\) is \(k\)-entire colorable. Let \(G\) be an outerplane graph with maximum degree \(\Delta\) and the entire chromatic number \(\chi_{\text{vef}}(G)\). This paper proves that if \(\Delta\geq6\), then \(\Delta+1\leq\chi_{\text{vef}}(G)\leq\Delta+2\), and \(\chi_{\text{vef}}(G)\leq\Delta+1\) if and only if \(G\) has a matching consisting of some inner edges which covers all its vertices of maximum degree.
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 5008215
zbMATH Keywords: colors
author: Weifan Wang
author: Keming Zhang
reviewed by: Stanislav Jendroľ
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30207-2
OpenAlex ID: W2479859028
description: scientific article; zbMATH DE number 5008215