Decomposing weighted digraphs into sums of chains
Let \(W=[W_{ij}]\) denote an \(n\times n\) matrix of non-negative integers such that \(W_{ii}=0\) for all i and \(W_{ij}+W_{ji}=m\) for all distinct i and j. When does there exist a set of m rankings of n objects such that object i is ranked ahead of object j in precisely \(W_{ij}\) rankings? The author gives conditions that are necessary and sufficient for this to be the case if \(m\leq 2\) or \(n\leq 5\).
scientific article; zbMATH DE number 3979086
scientific article