Three moves on signed surface triangulations
type: Item
instance of: scholarly article
title: Three moves on signed surface triangulations
zbMATH Open document ID: 1025.05014
author: Shalom Eliahou
author: Sylvain Gravier
author: Charles Payan
published in: Journal of Combinatorial Theory. Series B
publication date: 2002-12-10T00:00:00Z
review text: A finite triangulation of a surface with \(-1\) or \(+1\) assigned to each face has the Heawood property if the sum of the assignments to the faces incident with vertex \(x\) is divisible by \(3\), for every \(x\). The authors introduce three moves on signed surface triangulations that preserve the Heawood property, and they prove that every Heawood signed triangulation of the sphere can be obtained from a Heawood signed triangle, by a sequence of the three moves. Applications are given to 4-vertex-colorings of planar graphs.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1843804
zbMATH Keywords: vertex-colorings
zbMATH Keywords: Heawood property
zbMATH Keywords: planar graphs
reviewed by: Arthur T. White
MaRDI profile type: Publication
OpenAlex ID: W2050619547
cites work: Every planar map is four colorable. I: Discharging
cites work: Every planar map is four colorable. II: Reducibility
cites work: Signed diagonal flips and the four color theorem
cites work: Q5620163
cites work: Q5839331
DOI: 10.1006/JCTB.2001.2066
description: scientific article; zbMATH DE number 1843804