  Given an infinite graph $\GI$ quasi-transitive and amenable with maximum
degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$
of the q-state antiferromagnetic Potts model at zero temperature on $\GI$ is
analytic in the variable 1/q, whenever $|2\D e^3/q|< 1$. This result proves, in
an even stronger formulation, a conjecture originally sketched in [KE] (Kim and
Enting, 1979) and explicitly formulated in [ST] (Shrock and Tsai,1997), based
on which a sufficient condition for $W_r(\GI,q)$ to be analytic at 1/q=0 is
that $\GI$ is a regular lattice.
