Long cycles in bipartite tournaments
type: Item
instance of: scholarly article
title: Long cycles in bipartite tournaments
zbMATH Open document ID: 0842.05040
DOI: 10.1016/0012-365X(94)00273-L
published in: Discrete Mathematics
publication date: 1996-03-24T00:00:00Z
review text: Let \(D\) be an oriented complete bipartite graph and \(d^+(u)\) \((d^-(u))\) the outdegree (indegree) of any vertex of \(D\). The digraph \(D\) satisfies condition \(C(n)\) if \(d^+(u)+ d^-(v)\geq n\) whenever \(uv\) is not an arc of \(D\). A \(p\times q\) bipartite tournament \(T\) is an oriented complete bipartite graph with bipartition \((X, Y)\) where \(|X|= p\) and \(|Y|= q\). The main result established is: if \(T\) is a \(p\times q\) strong bipartite tournament satisfying \(C(n)\), then \(T\) contains a cycle of length at least 2 \(\min (n+ 1, p, q)\) unless \(n\) is even and isomorphic to a specified family of graphs.
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 858086
zbMATH Keywords: loop
zbMATH Keywords: digraph
zbMATH Keywords: bipartite tournament
zbMATH Keywords: cycle
author: Jianzhong Wang
reviewed by: David P. Brown
MaRDI profile type: Publication
cites work: Cycles and paths of many lengths in bipartite digraphs
cites work: Degrees and Longest Paths in Bipartite Digraphs
cites work: Q5422499
cites work: Cycles and paths in bipartite tournaments with spanning configurations
cites work: Long paths and cycles in oriented graphs
cites work: Q3487412
full work available at URL: 0012-365x(94)00273-l
OpenAlex ID: W2090678880
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description: scientific article; zbMATH DE number 858086