In this paper, we first prove that the arboricity of the dual graph of
an arrangement of hyperplanes in $d$-dimensional Euclidian space is
$d$. The result is extended partially to the arrangement of
hypersurfaces. Also, we introduce a new measure of the complexity of
the dual graph of an arrangement, and bound it by only using the
property of the graph. This bound can be used in the analysis of a
computationally robust algorithm for Voronoi diagrams and also to
obtain another optimal randomized algorithm for finding the
intersections among line segments and curves.