Optimal packings of edge-disjoint odd cycles

In a simple graph, we consider the minimum number of edges which hit all the odd cycles and the maximum number of edge-disjoint odd cycles. When these two coefficients are equal, interesting questions can be posed. Related problems, but interchanging ‘vertex-disjoint’ and ‘edge-disjoint’, have been studied by Berge and Fouquet (Discrete Math. 169 (1997) 169–176.)