ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Mathematicae Graph Theory 20(2) (2000) 197-207 DOI: 10.7151/dmgt.1119
Instituto de Matemáticas, UNAM
Circuito Exterior, C.U.
México 04510 D.F., MÉXICO
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.
2000 Mathematics Subject Classification: 05C20, 05C15, 05C65.
Received 10 November 1999
Revised 30 October 2000