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 Galloet al.(G. Gallo, M. D. Grigoriadis, and R. E. Tarjan,SIAM J. Comput.18(1) (1989), 30–55). We compute the arboricity in timeO(nm log(n²/m)), the same bound as the other parametric flow algorithms of Galloet al.(nandmdenote the number of vertices and edges of the given graph, respectively). For graphs with integral capacities that areO(1) the time improves toO(m^3/2log(n²/m)). Finding a minimum-cost base solves problems like optimal reinforcement of a network. We find a base in timeO(n²m log(n²/m)), improving the previous bound ofmmaximum flow computations. The fractional packing number is known as the strength of a network. We compute it in timeO(n²m log(n²/m)) and spaceO(m), improving the best previous result by a factornin 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-sets.