Unimodularity and circle graphs
type: Item
instance of: scholarly article
title: Unimodularity and circle graphs
zbMATH Open document ID: 0647.05039
DOI: 10.1016/0012-365X(87)90132-4
author: André Bouchet
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: A property of unimodularity is introduced for antisymmetric integral matrices. It is satisfied by the adjacency matrix of a circle graph provided with a Naji orientation [\textit{W. Naji}, Discrete Math. 54, 329- 337 (1985; Zbl 0567.05033)]. In a further paper we shall interprete this result in terms of symmetric matroids introduced in the author's paper in Math. Program. 38, 147-159 (1987; Zbl 0633.90089). In this communication we give a direct proof by means of techniques used in the author's paper in C. R. Acad. Sci., Paris, Ser. A 274, 724-727 (1972; Zbl 0228.05104), for an algorithmic solution of the Gauss problem on self-intersecting curves in the plane.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4055655
zbMATH Keywords: unimodularity
zbMATH Keywords: antisymmetric integral matrices
MaRDI profile type: Publication
cites work: Q5635462
cites work: Greedy algorithm and symmetric matroids
cites work: Characterization of Totally Unimodular Matrices
cites work: Local complementation and interlacement graphs
cites work: Q3328583
cites work: Q3222218
cites work: Reconnaissance des graphes de cordes
cites work: Lectures on matroids
full work available at URL: 0012-365x(87)90132-4
OpenAlex ID: W2090799803
description: scientific article; zbMATH DE number 4055655