On the connectivity function of a binary matroid
type: Item
instance of: scholarly article
title: On the connectivity function of a binary matroid
zbMATH Open document ID: 1025.05013
author: Manoel Lemos
published in: Journal of Combinatorial Theory. Series B
publication date: 2002-12-10T00:00:00Z
review text: The connectivity function of a matroid \(M\) is defined as \(\xi_M(X,Y)= r_M(X)+ r_M(Y)- r(M)+1\) where \(\{X,Y\}\) is a partition of the ground set \(E(M)\). Cunningham conjectured that if \(M\) and \(N\) are connected matroids on the same ground set having the same connectivity function, then \(N= M\) or \(N= M^*\). \textit{P. D. Seymour} [J. Comb. Theory, Ser. B 45, 25-30 (1988; Zbl 0671.05022)] gave a counterexample to the general case of this conjecture and proved it for the class of binary matroids. In this paper, the author proves that a connected binary matroid is reconstructible, not only in the class of binary matroids, but also in the class of all matroids. That is, if \(M\) is a connected binary matroid and \(N\) is a matroid having the same connectivity function as \(M\) and \(E(M)= E(N)\), then \(N= M\) or \(N= M^*\).
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1843847
zbMATH Keywords: connectivity function
zbMATH Keywords: matroids
reviewed by: Jorge Luis Ramírez Alfonsín
MaRDI profile type: Publication
full work available at URL: jctb.2002.2118
OpenAlex ID: W2050840929
cites work: Matroids having the same connectivity function
cites work: Non-Binary Matroids Having At Most Three Non-Binary Elements
cites work: The reconstruction of a matroid from its connectivity function
cites work: A Matroid Reconstruction Result
cites work: Q4198526
cites work: A characterization of a class of non-binary matroids
cites work: Q3135082
cites work: Q4717848
cites work: The smallest rounded sets of binary matroids
cites work: Decomposition of regular matroids
cites work: On the connectivity function of a matroid
cites work: Connectivity in Matroids
DOI: 10.1006/JCTB.2002.2118
description: scientific article; zbMATH DE number 1843847