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P.D. Seymour proved that the cut criterion is necessary and su cient for the solvability of the edgedisjoint paths problem when the union of the supply graph and the demand graph is planar and Eulerian. When only planarity is required, M. Middendorf and F. Pfei er proved the problem to be NP-complete. For this case E. Korach and M. Penn proved that the cut criterion is su cient for the existence of a near-complete packing of paths. Here we generalize this result by showing how a naturaldoi:10.1007/bf01585937 fatcat:a5njs2efrjhojfipc66snef55i