Summary: We present efficient algorithms for finding the covering number, finding a base, and finding the packing number, all in graphic polymatroids. The integral covering number is the arboricity of an undirected graph; computing it is suggested as an open problem by G. Gallo, M. D. Grigoriadis, and R. E. Tarjan [SIAM J. Comput. 18, No. 1, 30-55 (1989; Zbl 0679.68080)]. We compute the arboricity in time \(O(nm \log (n^2/m))\), the same bound as the other parametric flow algorithms of Gallo et al. \((n\) and \(m\) denote the number of vertices and edges of the given graph, respectively). For graphs with integral capacities that are \(O(1)\) the time improves to \(O(m^{3/2} \log (n^2/m))\). Finding a minimum-cost base solves problems like optimal reinforcement of a network. We find a base in time \(O(n^2m \log (n^2/m))\), improving the previous bound of \(m\) maximum flow computations. The fractional packing number is known as the strength of a network. We compute it in time \(O(n^2m \log (n^2/m))\) and space \(O(m)\), improving the best previous result by a factor \(n\) in space. Our algorithms are based on a new characterization of the vectors in a graphic polymatroid, and also on an extension of parametric flow techniques to a problem concerning global minimum cuts, called parametric augmentation for \(\overline s\)-sets.