Geodesic
Dichromatic number, circulant tournaments and Zykov sums of digraphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 197-207

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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 H₁(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.
Keywords: digraphs, dichromatic number, vertex-critical, Zykov sums, tournaments, circulant, covering numbers in hypergraphs 
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     title = {Dichromatic number, circulant tournaments and {Zykov} sums of digraphs},
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Neumann-Lara, Víctor. Dichromatic number, circulant tournaments and Zykov sums of digraphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 197-207. http://geodesic.mathdoc.fr/item/DMGT_2000_20_2_a3/