A sufficient condition for planar graphs to be 3-colorable
type: Item
instance of: scholarly article
title: A sufficient condition for planar graphs to be 3-colorable
zbMATH Open document ID: 1023.05046
DOI: 10.1016/S0095-8956(03)00025-X
published in: Journal of Combinatorial Theory. Series B
publication date: 2003-08-25T00:00:00Z
review text: The authors prove that every proper 3-coloring of a face of size 3 or 7 in a connected planar graph without pairs of 3-cycles at distance less than 4 and without 5-cycles can be extended to a proper 3-coloring of the whole graph. Form this and Grötzsch's theorem, it follows that planar graphs without 3-cycles at distance less than 4 and without 5-cycles are 3-colorable. The authors conjecture that planar graphs without 5-cycles in which every two 3-cycles are vertex-disjoint (or every two 3-cycles are edge-disjoint) are 3-colorable.
reviewed by: Van Bang Le
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1970673
zbMATH Keywords: graph coloring
author: Oleg V. Borodin
author: André Raspaud
MaRDI profile type: Publication
cites work: Some simplified NP-complete graph problems
cites work: On a conjecture of B. Grünbaum
cites work: 25 pretty graph colouring problems
cites work: Q3139765
full work available at URL: s0095-8956(03)00025-x
OpenAlex ID: W2104261748
description: scientific article; zbMATH DE number 1970673