Stability in the Erdős-Gallai Theorem on cycles and paths, II

In this paper, we complete a stability theorem which strengthens Kopylov's result. In particular, we show that for k≥3 odd and all n≥k, every n-vertex 2-connected graph G with no cycle of length at least k is a subgraph of one of the two extremal graphs or e(G)≤max{h(n,k,3),h(n,k,k−32)}. The upper bound for e(G) here is tight.