We prove that the motion of a single hole induces the nearest-neighbor
resonating-valence-bond ground state in the U=β Hubbard model on a
triangular cactus - a tree-like variant of a kagome lattice. The result can be
easily generalized to tβJ models with antiferromagnetic interactions Jβ₯0 on the same graphs. This is a weak converse of Nagaoka's theorem of
ferromagnetism on a bipartite lattice.Comment: 4 pages + references, a revised versio