Two proofs of the Bermond-Thomassen conjecture for tournaments with bounded minimum in-degree
type: Item
instance of: scholarly article
title: Two proofs of the Bermond-Thomassen conjecture for tournaments with bounded minimum in-degree
zbMATH Open document ID: 1188.05072
author: Nicolas Lichiardopol
author: Jean-Sébastien Sereni
author: Stéphane Bessy
published in: Discrete Mathematics
publication date: 2010-03-29T00:00:00Z
review text: In 1981, \textit{J.C. Bermond} and \textit{C. Thomassen} [``Cycles in digraphs. A survey'', J. Graph Theory 5, 1--43 (1981; Zbl 0458.05035)] conjectured that for any positive integer \(r\), any digraph of minimum out-degree at least \(2r - 1\) contains at least r vertex-disjoint directed cycles. It can be shown that the conjecture is true for \(r = 2\) and \(3\), and that a \(k\)-strongly-connected tournament of order at least \(5k - 3\) contains \(k\) vertex-disjoint directed cycles. The present note gives two proofs of this conjecture for tournaments with minimum in-degree at least \(2r - 1\).
reviewed by: Wai-Kai Chen
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 5687590
zbMATH Keywords: digraph
zbMATH Keywords: tournament
zbMATH Keywords: cycle
zbMATH Keywords: degree
Wikidata QID: Q123286770
MaRDI profile type: Publication
full work available at URL: j.disc.2009.03.039
OpenAlex ID: W2069056401
cites work: Q4500916
cites work: Cycles in digraphs– a survey
cites work: Partitioning vertices of a tournament into independent cycles
cites work: The partition of a strong tournament
cites work: Disjoint cycles in digraphs
DOI: 10.1016/J.DISC.2009.03.039
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description: scientific article; zbMATH DE number 5687590