Invariant subspaces and generalization of Nagaoka's theorem for the Hubbard model (U=∞)

The hubbard model (U=∞) on an arbitrary graph of sites in the presence of one hole in the system is considered. A sufficient condition for the absence of invariant subspaces of the space of states with fixed value of thez projection of the total spin that differ in the sets of possible spin configurations is found. A generalization of Nagaoka's results for bilobate graphs is given.