On cycles through a given vertex in multipartite tournaments
type: Item
instance of: scholarly article
title: On cycles through a given vertex in multipartite tournaments
zbMATH Open document ID: 0883.05087
DOI: 10.1016/S0012-365X(96)00048-9
author: Yubao Guo
author: Axel Pinkernell
author: Lutz Volkmann
published in: Discrete Mathematics
publication date: 1997-06-10T00:00:00Z
review text: An \(n\)-partite tournament is a directed graph obtained from a complete \(n\)-partite graph by assigning directions to its edges. The authors show that if \(D\) is a strongly connected \(n\)-partite tournament with partite sets \(V_1,V_2,\dots, V_n\) and \(v\) is an arbitrary vertex of \(D\), then (1) \(v\) belongs to some longest cycle of \(D\), (2) if \(n\geq 3\), then \(v\) belongs to an \(m\)- or \((m+1)\)-cycle for every \(m\in \{3,4,\dots,n\}\), (3) if \(n\geq 4\) and \(|V_i|\geq 2\) for \(i=1,2,\dots,n\), then \(v\) belongs to an \((n+1)\)- or \((n+2)\)-cycle of \(D\). Known results due to Bondy, Ayel and Gutin are then deduced from these results.
reviewed by: Ortrud R. Oellermann
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 1019059
zbMATH Keywords: tournament
zbMATH Keywords: longest cycle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1019059