Matchings and \(\Delta\)-matroids
type: Item
instance of: scholarly article
title: Matchings and \(\Delta\)-matroids
zbMATH Open document ID: 0708.05014
DOI: 10.1016/0166-218X(92)90272-C
author: André Bouchet
published in: Discrete Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: [This is a joint review for the paper mentioned above [Zbl 0708.05013] (first paper) and this one (second paper).] In these important papers the author introduces a very interesting structure and proves a lot of beautiful results. Let \(\Delta\) denote symmetric difference and replace \(\setminus\) by \(\Delta\) in the matroid base axiom ``For X,Y\(\in {\mathcal F}\) and \(x\in X\setminus Y\) there exists a \(y\in Y\setminus X\) such that \(X\Delta\{\) x,y\(\}\in {\mathcal F}.''\) Hence a generalization of matroids, called \(\Delta\)-matroids, is introduced. The first paper presents results on representing \(\Delta\)-matroids by antisymmetric matrices, on their relations with Eulerian tours of 4- regular graphs, with matroids introduced by Dress and Havel, and with electrically self-dual matroids, introduced by the reviewer. The second paper characterizes \(\Delta\)-matroids via a greedy algorithm, studies the relations between matchings and \(\Delta\)-matroids, and defines the union of \(\Delta\)-matroids and the induction of \(\Delta\)-matroids by a bipartite graph.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4162894
zbMATH Keywords: Delta-matroids
zbMATH Keywords: symmetric difference
zbMATH Keywords: matroid base
zbMATH Keywords: greedy algorithm
zbMATH Keywords: matchings
zbMATH Keywords: union
zbMATH Keywords: induction
zbMATH Keywords: bipartite graph
reviewed by: András Recski
MaRDI profile type: Publication
cites work: The perfectly matchable subgraph polytope of a bipartite graph
cites work: Greedy algorithm and symmetric matroids
cites work: Comments on bases in dependence structures
cites work: Paths, Trees, and Flowers
cites work: Q5684698
cites work: The dependence graph for bases in matroids
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cites work: Matching theory
cites work: The Factorization of Linear Graphs
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description: scientific article; zbMATH DE number 4162894