Edge-disjoint odd cycles in graphs with small chromatic number

For a simple graph, we consider the minimum number of edges which block all the odd cycles and the maximum number of odd cycles which are pairwise edg e-disjoint. When these two coefficients are equal, interesting consequences appear. Similar problems (but interchanging "vertex-disjoint odd cycles" a nd "edge-disjoint odd cycles") have been considered in a paper by Berge and Fouquet.