Hamilton decompositions of directed cubes and products

AbstractCall a directed graph G↔ symmetric if it is obtained from an undirected graph G by replacing each edge of G by two directed edges, one in each direction. We will show that if G has a Hamilton decomposition with certain additional structure, then G↔×C↔n×K↔2 has a directed Hamilton decomposition. In particular, it will follow that the bidirected cubes Q↔2m+1 for m⩾2 are decomposable into 2m+1 directed Hamilton cycles and that a product of cycles C↔n1×⋯×C↔nm×K↔2 is decomposable into 2m+1 directed Hamilton cycles if ni⩾3 and m⩾2