2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125592We consider nearest-neighbor fertile hard-core models, with three states, on a homogeneous Cayley tree. It is known that there are four type of such models. We investigate all of them and describe translation-invariant and periodic hard-core Gibbs measures. Also we construct a continuum set of non-periodic Gibbs measures.13 pagesMathematical PhysicsProbability82C26text