On a characterization of Gauss codes
type: Item
instance of: scholarly article
title: On a characterization of Gauss codes
zbMATH Open document ID: 0932.05024
DOI: 10.1007/PL00009461
published in: Discrete \& Computational Geometry
publication date: 1999-12-15T00:00:00Z
review text: The traversal of a self-crossing closed plane curve, with points of multiplicity at most two and with only a finite number of multiple points, defines a double occurrence sequence, the Gauss code of the curve. Given a sequence \(S\), two symbols \(u,v\) are said to be interlaced in \(S\) if exactly one occurrence of \(v\) appears in \(S\) between the two occurences of \(u\). This relation gives rise to the interlacement graph of \(S\), \(\Lambda (S)\). \textit{P. Rosenstiehl} [C. R. Acad. Sci., Paris, Sér. A 283, 551-553 (1976; Zbl 0345.05130)] characterized Gauss codes by \(\Lambda (S)\). Introducing a switch operation, the authors give a new characterization of these sequences by \(\Lambda (S)\) and then deduce a simple self-contained proof of Rosenstiehl's characterization.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 1334944
zbMATH Keywords: Gauss code
zbMATH Keywords: Eulerian graph
zbMATH Keywords: switching operation
author: Hubert de Fraysseix
author: P. Ossona de Mendez
MaRDI profile type: Publication
full work available at URL: pl00009461
OpenAlex ID: W1503792772
description: scientific article; zbMATH DE number 1334944