  The MEG (minimum equivalent graph) problem is, given a directed graph, to
find a small subset of the edges that maintains all reachability relations
between nodes. The problem is NP-hard. This paper gives a proof that, for
graphs where each directed cycle has at most three edges, the MEG problem is
equivalent to maximum bipartite matching, and therefore solvable in polynomial
time. This leads to an improvement in the performance guarantee of the
previously best approximation algorithm for the general problem in
``Approximating the Minimum Equivalent Digraph'' (1995).
