A conjecture of Neumann-Lara on infinite families of r-dichromatic circulant tournaments

In this paper we exhibit infinite families of vertex critical r-dichromatic circulant tournaments for all r ≥ 3. The existence of these infinite families was conjectured by NeumannLara (7), who later proved it for all r ≥ 3 and r 6= 7. Using different methods we find explicit constructions of these infinite families for all r ≥ 3, including the case when r = 7, which complets the proof of the conjecture.