  We consider the standard repulsive Hubbard model with a flat lowest-energy
band for two one-dimensional lattices (diamond chain and ladder) as well as for
a two-dimensional lattice (bilayer) at half filling of the flat band. The
considered models do not fall in the class of Mielke-Tasaki flat-band
ferromagnets, since they do not obey the connectivity conditions. However, the
ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To
study this kinetic-energy-driven ferromagnetism we use perturbation theory and
exact diagonalization of finite lattices. We find as a typical scenario that
small and moderate dispersion may lead to a ferromagnetic ground state for
sufficiently large on-site Hubbard repulsion $U>U_c$, where $U_c$ increases
monotonically with the acquired bandwidth. However, we also observe for some
specific parameter cases, that (i) ferromagnetism appears at already very small
$U_c$, (ii) ferromagnetism does not show up at all, (iii) the critical on-site
repulsion $U_c$ is a nonmonotonic function of the bandwidth, or that (iv) a
critical bandwidth is needed to open the window for ground-state
ferromagnetism.
