We prove that the motion of a single hole induces the nearest-neighbor resonating-valence-bond ground state in the $U=\infty$ 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 $J\ge 0$ on the same graphs. This is a weak converse of Nagaoka's theorem of ferromagnetism on a bipartite lattice.

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• Quantum spin liquid
• Hubbard model
• Resonating valence bond theory