  We construct a basis for the many-particle ground states of the positive
hopping Bose-Hubbard model on line graphs of finite 2-connected planar
bipartite graphs at sufficiently low filling factors. The particles in these
states are localized on non-intersecting vertex-disjoint cycles of the line
graph which correspond to non-intersecting edge-disjoint cycles of the original
graph. The construction works up to a critical filling factor at which the
cycles are close-packed.
