The acyclic disconnection of a digraph

In this paper we introduce a numerical invariant of digraphs which generalizes that of the number of connected components of a graph. The ao,clic disconnection ~(D) of a digraph D is the minimum number of (weakly) connected components of the subdigraphs obtained from D by deleting an acyclic set of arcs. We state some results about this invariant and compute its value for a variety of circulant tournaments. Relations between the dichromatic number and the acyclic disconnection of digraphs are explored and a generalization of the second invarianl is presented. @ 1999 Elsevier Science B.V. All rights reserved A MS classification. Primary: 05C20; 05C 15 K~:vwords. Digraphs; Tournaments; Connectedness; Acyclic disconnection; Vertex colourings: Dichromatic number