Exact hole-induced resonating-valence-bond ground state in certain U = ∞ Hubbard models

We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the U = oo Hubbard model on a triangular cactus-a treelike variant of a kagome lattice. The result can be easily generalized to t - J models with antiferromagnetic interactions J 0 on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice.