Autonomous parts and decomposition of regular tournaments
type: Item
instance of: scholarly article
title: Autonomous parts and decomposition of regular tournaments
zbMATH Open document ID: 0785.05043
DOI: 10.1016/0012-365X(93)90137-I
author: Annie Astié-Vidal
author: Vincent Dugat
published in: Discrete Mathematics
publication date: 1994-04-05T00:00:00Z
review text: The weight of an arc in a tournament is the number of 3-cycles containing the arc. Two vertices \(x\) and \(y\) of a regular tournament are \(W\)- equivalent if the arcs directed towards (away from) \(x\) have the same weights as the arcs directed towards (away from) \(y\), respectively. The authors' main aim is to obtain some results on arc-weights for regular tournaments with a non-trivial subset \(S\) of vertices such that for every vertex \(y\) not in \(S\) either \(y\) dominates or is dominated by every vertex in \(S\); particular emphasis is given to such tournaments \(S\) all of whose vertices are \(W\)-equivalent.
reviewed by: J. W. Moon
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 428295
zbMATH Keywords: 3-cycles
zbMATH Keywords: regular tournaments
MaRDI profile type: Publication
cites work: Near-homogeneous tournaments and permutation groups
cites work: Q4729814
cites work: Q5615282
cites work: Q5530476
cites work: Q5588447
cites work: Q5585195
cites work: On strongly homogeneous tournaments
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cites work: Doubly regular tournaments are equivalent to skew Hadamard matrices
cites work: Caracterisation Des Tournois Presqu'Homogenes
cites work: Q3691703
full work available at URL: 0012-365x(93)90137-i
OpenAlex ID: W1968168206
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description: scientific article; zbMATH DE number 428295