Counterexamples to Adám's conjecture on arc reversals in directed graphs
type: Item
instance of: scholarly article
title: Counterexamples to Adám's conjecture on arc reversals in directed graphs
zbMATH Open document ID: 0609.05041
DOI: 10.1016/0095-8956(87)90068-2
author: Carsten Thomassen
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: The author defines an infinite class of directed graphs with the property that reversing any arc increases the length of a longest directed cycle. From this he obtains counterexamples to Adám's conjecture that any directed graph with at least one directed cycle contains an arc whose reversal decreases the total number of directed cycles.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3985258
zbMATH Keywords: arc reversals
zbMATH Keywords: directed graphs
zbMATH Keywords: longest directed cycle
zbMATH Keywords: Adám's conjecture
zbMATH Keywords: number of directed cycles
reviewed by: J. W. Moon
MaRDI profile type: Publication
full work available at URL: 0095-8956(87)90068-2
OpenAlex ID: W1983352634
cites work: Q3955369
cites work: Bemerkungen zum graphentheoretischen Satze von I. Fidrich
cites work: Q5672928
cites work: Q3872493
cites work: Cycles in digraphs– a survey
cites work: Q5422499
cites work: When the cartesian product of two directed cycles is hypo-Hamiltonian
cites work: Q3220616
cites work: Q4146745
description: scientific article; zbMATH DE number 3985258