Let us show that the labelling algorithm of Ford and Fulkerson (Algorithm 6.1.7) may be viewed as a special case of Algorithm 10.3.13. We choose for e0 the return arc r = ts introduced in Example 10.1.1, and color e0 black. The remaining edges e are colored as follows: black if e is void, green if e is saturated, and red otherwise. It should be clear that case (1) of the painting lemma then yields an augmenting path from s to t, whereas in case (2) no such path exists. Then the cocycle constructed by the algorithm corresponds to a minimal cut of N (with capacity equal to the value of the maximal flow f).