On prisms, Möbius ladders and the cycle space of dense graphs

All these degree-conditions are essentially best-possible. The implications in (1) and (2) give an asymptotic affirmative answer to a special case of an open conjecture which according to [I.B.-A. Hartman, Long cycles generate the cycle space of a graph, European J. Combin. 4 (3) (1983) 237-246] originates with A. Bondy.