Packing edge-disjoint cycles in graphs and the cyclomatic number

For a graph G let μ(G) denote the cyclomatic number and let ν(G) denote the maximum number of edge-disjoint cycles of G.We prove that for every k≥0 there is a finite set P(k) such that every 2-connected graph G for which μ(G)−ν(G)=k arises by applying a simple extension rule to a graph in P(k). Furthermore, we determine P(k) for k≤2 exactly.