Abstract
The acyclic disconnectionω→(D)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overrightarrow{\\omega }(D)$$\\end{document} of a digraph D is the maximum possible number of (weakly) connected components of a digraph obtained from D by deleting an acyclic set of arcs. In this paper, we provide new lower and upper bounds in terms of properties such as the degree, the directed girth, and the existence of certain subdigraphs and bounds for bipartite digraphs, p-cycles, and some circulant digraphs. Finally, as a consequence of our bounds, we prove the Conjecture of Caccetta and Häggkvist for a particular class of digraphs.
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