Whitney's 2-switching theorem, cycle spaces, and arc mappings of directed graphs

AbstractWe establish a directed analogue of Whtney's 2-switching theorem for graphs and apply it to settle the problem [J. London Math. Soc. (2) 3 (1971), 378–384] of Goldberg and Moon by showing that a strong tournament is uniquely determined, up to isomorphism or anti-isomorphism, by its arc set together with those arc sets that form directed 4-cycles. We obtain the corresponding result for directed Hamiltonian cycles in 1015-connected tournaments. The proofs are based on investigations of the cycle space of a tournament