Minimally 4-edge\(^ \#\)-connected graphs
type: Item
instance of: scholarly article
title: Minimally 4-edge\(^ \#\)-connected graphs
zbMATH Open document ID: 0802.05050
DOI: 10.1016/0012-365X(94)90170-8
author: B. Péroche
author: Christine Virlouvet
published in: Discrete Mathematics
publication date: 1994-12-01T00:00:00Z
review text: The \(\text{edge}^ \#\)-connectivity of a graph \(G\), defined by \textit{S. B. Maurer} and \textit{P. J. Slater} [Discrete Math. 24, 185-195 (1978; Zbl 0397.05033)], is the minimum cardinality of a cutset \(S\), if one exists, such that \(G-S\) has exactly two components, each containing at least one edge. The paper characterizes some minimally 4-\(\text{edge}^ \#\)- connected graphs, i.e., graphs with \(\text{edge}^ \#\)-connectivity 4, where the deletion of every edge decreases the \(\text{edge}^ \#\)- connectivity.
reviewed by: Martin Škoviera
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 562673
zbMATH Keywords: edge-connectivity
zbMATH Keywords: minimally \(k\)-connected graph
MaRDI profile type: Publication
cites work: Q4096964
cites work: A Construction Method For Minimally K-Edge-Connected Graphs
cites work: Conditional connectivity
cites work: A Reduction Method for Edge-Connectivity in Graphs
cites work: On k-minimally n-edge-connected graphs
cites work: On several sorts of connectivity
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description: scientific article; zbMATH DE number 562673