Infinite families of (n+1)-dichromatic vertex critical circulant tournaments

In this talk we expose the results about infinite families of vertex critical r-dichromatic circulant tournaments for all r ≥ 3. The existence of these infinite families was conjectured by Neumann-Lara [6], who later proved it for all r ≥ 3 and r = 7. Using different methods we find explicit constructions of these infinite families for all r ≥ 3, including the case when r = 7, which complete the proof of the conjecture.