The regular matroids with no 5-wheel minor
type: Item
instance of: scholarly article
title: The regular matroids with no 5-wheel minor
zbMATH Open document ID: 0626.05009
DOI: 10.1016/0095-8956(89)90051-8
author: James Oxley
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: For r in \(\{\) 3,4\(\}\), the class of binary matroids with no minor isomorphic to M(\({\mathcal W}_ r)\), the rank-r wheel, has an easily- described structure. This paper determines all graphs with no \({\mathcal W}_ 5\)-minor and uses this to show that the class of regular matroids with no M(\({\mathcal W}_ 5)\)-minor also has a relatively simple structure. It is deduced from the graph result that a simple n-vertex graph having no \({\mathcal W}_ 5\)-minor has chromatic number at most 5. Moreover, such a graph has at most 3n-5 edges if \(n\equiv 2\) (mod 3) and has at most 3n-6 edges otherwise.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 4016914
zbMATH Keywords: binary matroids with no minor
zbMATH Keywords: regular matroids
zbMATH Keywords: graph
zbMATH Keywords: chromatic number
zbMATH Keywords: excluded minor
zbMATH Keywords: wheel graph
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90051-8
OpenAlex ID: W2035851622
cites work: Q3097395
cites work: A New Proof of a Theorem of Dirac
cites work: A Combinatorial Model for Series-Parallel Networks
cites work: A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs
cites work: In abstrakten Graphen vorhandene vollständige 4‐Graphen und ihre Unterteilungen
cites work: Some Results Concerning the Structure of Graphs
cites work: Topology of series-parallel networks
cites work: A characterization of 3-connected graphs containing a given graph
cites work: On 3-Connected Matroids
cites work: A characterization of the ternary matroids with no \(M(K_ 4)\)-minor
cites work: The Binary Matroids With No 4-Wheel Minor
cites work: Decomposition of regular matroids
cites work: Q3220598
cites work: Q3284374
cites work: Lectures on matroids
cites work: Connectivity in Matroids
cites work: On the chromatic number of binary matroids
cites work: Q4111952
description: scientific article; zbMATH DE number 4016914