Dichromatic number, circulant tournaments and Zykov sums of digraphs
Vı́ctor Neumann-Lara · Discussiones Mathematicae Graph Theory · 2000
The dichromatic number dc(D) of a digraph D is the smallest number of colours needed to colour the vertices of D so that no monochromatic directed cycle is created.In this paper the problem of computing the dichromatic number of a Zykov-sum of digraphs over a digraph D is reduced to that of computing a multicovering number of an hypergraph H 1 (D) associated to D in a natural way.This result allows us to construct an infinite family of pairwise non isomorphic vertex-critical k-dichromatic circulant tournaments for every k ≥ 3, k = 7.