Number of mincuts of a graph without using Karger's algorithm We know that Karger's mincut algorithm can be used to prove (in a non-constructive way) that the maximum number of possible mincuts a graph can have is $n \choose 2$.

I was wondering if we could somehow prove this identity by giving a bijective (rather injective) proof from the set of mincuts to another set of cardinality $n \choose 2$. No specific reasons, its just a curiosity. I tried doing it on my own but so far have not had any success. I would not want anyone to squander time over this and so if the question seems pointless I would request the moderators to take action accordingly.

Best
-Akash
The $\binom{n}{2}$ bound I think was originally proven by Dinitz, Karzanov and Lomonosov in 1976, in "A structure for the system of all minimum cuts of a graph".  Perhaps you can find what you're looking for in this paper, but I'm not sure if it's online.