algorithm - Are there more than one families of flow networks with non unique minimum cuts? -


i'm wondering if way construct flow network several minimum cuts include @ least 2 consecutive edges same capacity, such 1 of them in minimum cut edge set.

it's clear simplest kind of such network path edges of same capacity, in case 1 of |e| edges can edge separating s t.

is way construct such networks? if so, how can prove it?

i don't think true:

consider network:

a->b capacity 4 b->c capacity 2 a->c capacity 1 c->d capacity 3

we can either have cut (a,b,c)/(d) or (a,b)/(c,d) both cut of 3.

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