Indecomposability and duality of tournaments (Q1587596)

The authors say that a tournament \(T\) with \(n\) vertices is indecomposable if its vertex set cannot be partitioned into \(k\) subsets, where \(2\leq k\leq n-1\), in such a way that all of the arcs between any pair of subsets have the same orientation. They characterize tournaments \(T\) with the property that every proper subtournament of \(T\) that is indecomposable is also self-dual. They also consider the problem of reconstructing tournaments from their proper indecomposable subtournaments.