Graph representations of a bicircular matroid
type: Item
instance of: scholarly article
title: Graph representations of a bicircular matroid
zbMATH Open document ID: 0990.05025
DOI: 10.1016/S0166-218X(01)00210-4
author: Nancy Ann Neudauer
published in: Discrete Applied Mathematics
publication date: 2002-06-24T00:00:00Z
review text: The bicircular matroid \(B(G)\) of a graph \(G\) is known as a transversal matroid. The author discusses the graphs which represent the same bicircular matroid. The main results are: 1. The natural presentation of the bicircular matroid of a graph \(G\) determines \(G\) up to an isomorphism. 2. If \(G\) is a graph with no parallel edges and minimum degree at least three and \(G'\) is another graph such that \(B(G)= B(G')\), then \(G\) and \(G'\) are isomorphic. 3. Given any presentation for a bicircular matroid \(M\), then, up to isomorphism, the author describes an algorithm determining all the graphs \(G\) representing \(M\) such that \(B(G)=M\). 4. The description of the graphs arising from the minimal presentations of a bicircular matroid.
reviewed by: Mirela Ştefănescu
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C62
zbMATH DE Number: 1758380
zbMATH Keywords: transversal matroid
zbMATH Keywords: graph representation
MaRDI profile type: Publication
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full work available at URL: s0166-218x(01)00210-4
OpenAlex ID: W2153065381
description: scientific article; zbMATH DE number 1758380