  In 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.
