A splitter for graphs with no Petersen family minor
type: Item
instance of: scholarly article
title: A splitter for graphs with no Petersen family minor
zbMATH Open document ID: 0897.05029
author: John Maharry
published in: Journal of Combinatorial Theory. Series B
publication date: 1998-10-19T00:00:00Z
review text: The Petersen family consists of the seven graphs that can be obtained from the Petersen graph by \(Y\Delta\)- and \(\Delta Y\)-exchanges. A splitter for a family of graphs is a maximal 3-connected graph in the family. In this paper, a previously studied graph, \(Q_{13,3}\), is shown to be a splitter for the class of all graphs with no Petersen family minor. Moreover, \(Q_{13,3}\) is a splitter for the family of graphs with no \(K_6\)-minor, as well as for the family of graphs with no Petersen minor.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 1154564
zbMATH Keywords: Petersen family
zbMATH Keywords: Petersen graph
zbMATH Keywords: splitter
zbMATH Keywords: Petersen minor
MaRDI profile type: Publication
OpenAlex ID: W1986138218
cites work: Q3135082
cites work: Excluded minors in cubic graphs
cites work: Classification of minimal graphs of given face-width on the torus
cites work: Decomposition of regular matroids
cites work: Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface
DOI: 10.1006/JCTB.1997.1800
description: scientific article; zbMATH DE number 1154564