Basis pair graphs of transversal matroids are connected
type: Item
instance of: scholarly article
title: Basis pair graphs of transversal matroids are connected
zbMATH Open document ID: 0663.05058
DOI: 10.1016/0012-365X(89)90267-7
author: Martin Farber
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The basis pair graph of a matroid on the ground set S has, as its vertices, ordered triples of the form \((B_ 1,B_ 2,B_ 3)\), where \(B_ 1\) and \(B_ 2\) are disjoint bases and \(B_ 3=S\setminus (B_ 1\cup B_ 2)\). Two such vertices, \((A_ 1,A_ 2,A_ 3)\) and \((B_ 1,B_ 2,B_ 3)\), are adjacent if \((B_ 1,B_ 2,B_ 3)\) can be obtained from \((A_ 1,A_ 2,A_ 3)\) by interchanging two elements of S belonging to different components of \((A_ 1,A_ 2,A_ 3)\). It is known that basis pair graphs of graphic and cographic matroids are connected. We show that this holds for transversal matroids as well.
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4083683
zbMATH Keywords: basis pair graph
zbMATH Keywords: matroid
zbMATH Keywords: transversal matroids
MaRDI profile type: Publication
cites work: Some properties of basic families of subsets
cites work: An Affine Representation for Transversal Geometries
cites work: Edge‐disjoint spanning trees: A connectedness theorem
cites work: Decomposing symmetric exchanges in matroid bases
cites work: A Multiple Exchange Property for Bases
cites work: On the Tree Graph of a Matroid
cites work: Matroid basis graphs. I
cites work: Matroid basis graphs. II
cites work: An Exchange Theorem for Independence Structures
cites work: Q4111952
cites work: An exchange theorem for bases of matroids
description: scientific article; zbMATH DE number 4083683