Signed diagonal flips and the four color theorem
type: Item
instance of: scholarly article
title: Signed diagonal flips and the four color theorem
zbMATH Open document ID: 0938.05030
author: Shalom Eliahou
published in: European Journal of Combinatorics
publication date: 2000-06-21T00:00:00Z
review text: A flip of a diagonal \(e=uw\) in a plane triangulation \(T\) removes \(e\) from the quadrilateral \(uvwxu\) formed by the two faces of \(T\) adjacent to \(e\) and adds the opposite diagonal \(vx\). The author introduces a signed version of this operation, conjectures that any two triangulations of a given polygon can be transformed into each other by a signable sequence of diagonal flips, and shows that the conjectured statement would imply the four color theorem.
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1382656
zbMATH Keywords: plane triangulation
zbMATH Keywords: polygon
zbMATH Keywords: diagonal flips
zbMATH Keywords: four color theorem
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: eujc.1999.0312
OpenAlex ID: W2135735496
cites work: Combinatorial structure on triangulations. I: The structure of four colorings
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DOI: 10.1006/EUJC.1999.0312
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description: scientific article; zbMATH DE number 1382656