Autonomous parts and decomposition of regular tournaments
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.
scientific article; zbMATH DE number 428295
scientific article