In this paper we prove that for any integer $$q\ge 5$$
q
≥
5
, the anti-ferromagnetic q-state Potts model on the infinite $$\Delta $$
Δ
-regular tree has a unique Gibbs measure for all edge interaction parameters $$w\in [1-q/\Delta ,1)$$
w
∈
[
1
-
q
/
Δ
,
1
)
, provided $$\Delta $$
Δ
is large enough. This confirms a longstanding folklore conjecture.