Basic flow definitions

Residual network

Let [math]\displaystyle{ G=(V,A) }[/math] be a directed graph , [math]\displaystyle{ \ell(a) }[/math] and [math]\displaystyle{ u(a) }[/math] and [math]\displaystyle{ f(a)\in[\ell(a)\ldots u(a)] }[/math]

Flow-augmenting path

Let [math]\displaystyle{ G=(V,A)\lt /math be a directed graph , \lt math\gt \ell(a) }[/math] and [math]\displaystyle{ u(a) }[/math] and [math]\displaystyle{ f(a)\in[\ell(a)\ldots u(a)] }[/math]