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We prove that the motion of a single hole induces $SU(N)$ flavor-singlets inthe $U=\infty$ $SU(N)$ (Fermi) Hubbard model on a Husimi-like tree graph. Theresult is also generalized to certain $t$-$J$ models with antiferromagneticinteractions and singlet hopping terms typically neglected in the literature.This is an $SU(N)$ generalization of the "counter-Nagaoka theorem" introducedin [Phys. Rev. B 107, L140401 (2023)]. Our results suggest the existence ofantiferromagnetic or resonating-valence-bond (RVB)-like polarons in the $t$-$J$models on a more realistic non-bipartite lattice. Such antiferromagnetic/RVBpolarons may be relevant for a novel strong-coupling mechanism ofsuperconductivity or other exotic fractionalized phases of matter.

Exact hole-induced $SU(N)$ flavor-singlets in certain $U=\infty$ $SU(N)$ Hubbard models