  The visibility graph of a finite set of points in the plane has the points as
vertices and an edge between two vertices if the line segment between them
contains no other points. This paper establishes bounds on the edge- and
vertex-connectivity of visibility graphs.
  Unless all its vertices are collinear, a visibility graph has diameter at
most 2, and so it follows by a result of Plesn\'ik (1975) that its
edge-connectivity equals its minimum degree. We strengthen the result of
Plesn\'ik by showing that for any two vertices v and w in a graph of diameter
2, if deg(v) <= deg(w) then there exist deg(v) edge-disjoint vw-paths of length
at most 4. Furthermore, we find that in visibility graphs every minimum edge
cut is the set of edges incident to a vertex of minimum degree.
  For vertex-connectivity, we prove that every visibility graph with n vertices
and at most l collinear vertices has connectivity at least (n-1)/(l-1), which
is tight. We also prove the qualitatively stronger result that the
vertex-connectivity is at least half the minimum degree. Finally, in the case
that l=4 we improve this bound to two thirds of the minimum degree.
