  We model conducting pentagon chains with a multi orbital Hubbard model and
prove that well below half filling exact ferromagnetic ground states appear.
The rigorous method we use is based on the transformation of original
hamiltonian into positive semidefinite form. This technique is independent of
the spatial dimesion and does not require integrability of the model. The
obtained ferromagnetism is connected to dispersionless bands but in a much
broader sense than flat band ferromagnetism requires, where on every site a
Hubbard term is present. In our case only a small percentage of, even randomly
distributed, sites are only interacting.
