2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125077In a previous paper (From congruence identities to tolerance identities, in print on Acta Sci. Math. Szeged) we showed that, under certain conditions, a variety satisfies a given congruence identity if and only if it satisfies the same tolerance identity. Moreover, we mentioned that a parallel result holds for Mal'cev conditions arising from graphs. In the present note we give detailed definitions and state these more general results.5 pagesRings and Algebras08A30; 08B05text