There are possibly several min-cuts for the source and target nodes of a graph. I think I can determine the same min-cut for the same graph by putting the following restriction
"if there are several min-cuts, then I select the min-cut consisting of edges closer to the source atom. By saying close to source atom, I mean you start to travel from the source to the target, then an edge, which is in a min-cut you first encounter"
a,b and c are nodes, A, B and C are edges. The most left node is the source and the most right node is the target.
Example (1)
a --A--> b --B--> c
two sets: {A} and {B}. we chose {A}.
Example (2)
a --A--> b --B--> c
a --C--> d --D--> c
Four sets: {A, C}, {A,D},{C,B} and {B,D}. we chose {A, C}.
Example (3)
a --A--> b --B--> c
a --C--> b --D--> c
Two sets: {A,C} and {B,D}, we choose {A,C}.
We can keep trying, but I think all other graphs are combinations of these 3 examples (I may be missing some cases).
(1) So, I want to prove that by doing that way, I alway find a same min-cut for the same graph if I run the algorithm many times.
If I am right, how can I prove (1)?
or I am thinking too much about a very obvious fact? (^&^)
