  It is well known that the Hubbard model on a line graph has a flat band and
ferromagnetic ground states in a certain density range. We show that for a
Hubbard model on a line graph of a planar bipartite graph the ferromagnetic
ground state is stable if one adds a special contribution to the kinetic energy
which lifts the degeneracy of the lowest single particle state. Stability holds
for sufficiently strong repulsion U. The model has extended single particle
eigenstates, no degeneracy, and no band gap. It is therefore a good candidate
for metallic ferromagnetism.
