The delta-sum of matching delta-matroids
type: Item
instance of: scholarly article
title: The delta-sum of matching delta-matroids
zbMATH Open document ID: 0901.05025
DOI: 10.1016/S0012-365X(97)00044-7
author: André Bouchet
author: Werner Schwärzler
published in: Discrete Mathematics
publication date: 1998-11-26T00:00:00Z
review text: A delta-matroid is a pair \(D= (V,{\mathcal F})\), where \(V\) is a finite set and \({\mathcal F}\) is a nonempty collection of subsets of \(V\) satisfying the symmetric exchange axiom: For \(F_1,F_2\in{\mathcal F}\) and \(x\in F_1\Delta F_2\), there exists \(y\in F_1\Delta F_2\) such that \(F_1\Delta\{x, y\}\in{\mathcal F}\). The authors discuss a composition operation of delta-matroids, called delta-sum, namely: If \((V,{\mathcal F}_i)\), \(i= 1, 2\), are delta-matroids, then \((V,{\mathcal F}_1\Delta{\mathcal F}_2)\), where \({\mathcal F}_1\Delta{\mathcal F}_2= \{F_1\Delta F_2\mid F_1\in{\mathcal F}_1\) and \(F_2\in{\mathcal F}_2\}\), is also a delta-matroid. The delta-sum of matching delta-matroids is associated with the linkings of a graph. A min-max rank function of that delta-matroids, together with some applications of it on linkings are given in the last section of the paper.
reviewed by: Mirela Ştefănescu
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1135957
zbMATH Keywords: delta-matroid
zbMATH Keywords: symmetric exchange axiom
zbMATH Keywords: delta-sum
zbMATH Keywords: rank function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1135957