On a Conjecture of Víctor Neumann-Lara

We disprove the following conjecture due to Víctor Neumann-Lara: for every couple of integers (r,s) such that r≥s≥2 there is an infinite set of circulant tournaments T such that the dichromatic number and the acyclic disconnection of T are equal to r and s respectively. We show that for every integer s≥2 there exists a sharp lower bound b(s) for the dichromatic number r such that for every r