Counterexamples to a conjecture of Mader about cycles through specified vertices in \(n\)-edge-connected graphs
type: Item
instance of: scholarly article
title: Counterexamples to a conjecture of Mader about cycles through specified vertices in \(n\)-edge-connected graphs
zbMATH Open document ID: 0770.05067
DOI: 10.1007/BF02349962
author: Andreas Huck
author: Haruko Okamura
published in: Graphs and Combinatorics
publication date: 1993-01-16T00:00:00Z
review text: Providing counterexamples to a conjecture of Mader, the following theorem is proven: If \(n\geq 3\) is odd, then there exists an \(n\)-edge-connected graph \(G\) of order \(2^{(n+3)/2}\) which contains two vertices \(u\) and \(v\) at distance three such that, for each cycle \(C\) passing through \(u\) and \(v\), \(G-E(C)\) is not \((n-2)\)-edge-connected.
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 93441
zbMATH Keywords: \(n\)-edge-connected graph
zbMATH Keywords: counterexamples
zbMATH Keywords: conjecture of Mader
zbMATH Keywords: cycle
Wikidata QID: Q123115130
MaRDI profile type: Publication
cites work: Paths in graphs, reducing the edge-connectivity only by two
cites work: Paths and edge-connectivity in graphs
full work available at URL: https://doi.org/10.1007/bf02349962
OpenAlex ID: W2041509602
Recommended article: Proof of Mader's conjecture on k‐critical n‐connected graphs
Recommended article: A graph counterexample to Davies' conjecture
Recommended article: Q3481733
Recommended article: A generalization of Dirac's theorem on cycles through \(k\) vertices in \(k\)-connected graphs
Recommended article: Q3144345
Recommended article: A Conjecture of Verstraëte on Vertex-Disjoint Cycles
Recommended article: Counterexamples to three conjectures concerning perfect graphs
Recommended article: Q5046003
Recommended article: Cycles through large degree vertices in digraphs: A generalization of Meyniel's theorem
Recommended article: The confirmation of a conjecture on disjoint cycles in a graph
description: scientific article; zbMATH DE number 93441