2-reducible cycles containing three consecutive edges in \((2k+1)\)-edge- connected graphs
type: Item
instance of: scholarly article
title: 2-reducible cycles containing three consecutive edges in \((2k+1)\)-edge- connected graphs
zbMATH Open document ID: 0826.05042
DOI: 10.1007/BF01929484
author: Haruko Okamura
published in: Graphs and Combinatorics
publication date: 1995-08-27T00:00:00Z
review text: The author considers finite undirected multigraphs without loops and allows the repetition of vertices (but not of edges) in a path or cycle. Let \(G\) be a \(k\)-edge-connected graph and let \(f_0\), \(f_1\), \(f_2\) be its consecutive edges. A cycle \(C\) in \(G\) is called 2-reducible if \(G- E(C)\) is \((k- 2)\)-edge-connected. The author finds a nontrivial equivalent reformulation of the condition that no cycle in \(G\) containing \(f_0\), \(f_1\) and \(f_2\) is 2-reducible.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 784144
zbMATH Keywords: edge connected graph
zbMATH Keywords: multigraphs
zbMATH Keywords: path
zbMATH Keywords: cycle
reviewed by: Mikhail Ostrovskii
MaRDI profile type: Publication
cites work: On a theorem of Mader
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cites work: Q4273849
description: scientific article; zbMATH DE number 784144