On theories of Whitney and Tutte
type: Item
instance of: scholarly article
title: On theories of Whitney and Tutte
zbMATH Open document ID: 0584.05020
DOI: 10.1016/0012-365X(85)90163-3
author: Donald K. Wagner
published in: Discrete Mathematics
publication date: 1985-01-01T00:00:00Z
review text: By making extensive use of connectivity properties of graphs the author gives new proofs of the following classical results: (1) For nonseparable graphs G, G' the cycle matroids M(G) and M(G') are isomorphic iff G and G' are 2-isomorphic (Whitney); (2) A binary matroid M is graphic iff none of \(F_ 7\), \(F_ 7^*\), \(M^*(K_ 5)\) and \(M^*(K_{3,3})\) is a minor of M (Tutte). The proofs are simpler and shorter and such lend themselves for use in introductory courses on this subject.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 3935059
zbMATH Keywords: graphic matroid
zbMATH Keywords: connectivity properties of graphs
zbMATH Keywords: cycle matroids
MaRDI profile type: Publication
cites work: Q5422499
cites work: On matroid connectivity
cites work: Q3847747
cites work: Graphs, matroids, and geometric lattices
cites work: Decomposition of regular matroids
cites work: On Tutte's Characterization of Graphic Matroids
cites work: On Whitney's 2‐isomorphism theorem for graphs
cites work: Matroids and Graphs
cites work: Connectivity in Matroids
cites work: Q4111952
description: scientific article; zbMATH DE number 3935059