Whitney's 2-switching theorem, cycle spaces, and arc mappings of directed graphs
The author establishes a directed analogue of Whitney's 2-switching theorem which he uses in investigating the cycle space of tournaments. Let \(\pi\) denote a bijection between the arc-sets of two tournaments T and \(T'\). It is shown, among other things, that if T and \(T'\) are strong and \(\pi\) and \(\pi^{-1}\) preserve 4-cycles, then T and \(T'\) are isomorphic or anti-isomorphic; and if T and \(T'\) are \(10^{15}\)- connected and \(\pi\) and \(\pi^{-1}\) preserve Hamilton cycles, then \(\pi\) is induced by an isomorphism or an anti-isomorphism of T onto \(T'\).
scientific article; zbMATH DE number 4091536