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

Abstract

In this paper, we exhibit infinite families of vertex critical -dichromatic circulant tournaments for all . The existence of these infinite families was conjectured by Neumann-Lara [V. Neumann-Lara, Note on vertex critical 4-dichromatic circulant tournaments, Discrete Math. 170 (1997) 289–291], who later proved it for all and . Using different methods, we provide new constructions of such infinite families for all , which covers the case and thus settles the conjecture.