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

The hubbard model $(U=\infty)$ 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 the $z$ 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.