On a min-max conjecture for reducible digraphs

Abstract

A. Frank and A. Gyárfás (1976) have conjectured that in a reducible digraph D the maximum number of edge disjoint cycles equals the minimum number of edges intersecting all cycles of D. We prove this conjecture in the special case when D has at most two distinctdominators. The proof leads to a polynomial time algorithm for finding both the maximum set of cycles and minimum set of edges, in the considered case.