I'm currently studying a paper which uses extensively the term '
min-max theorems' in graph theory, and claims to present a tool allowing to generalize these theorems. (here is the link to the paper if needed)
Among those, we can find for example :
- The max-flow-min cut theorem.
- Edmond's disjoint arborescences theorem (link).
I have some intuition about what a min-max theorem would be, but I can't come with a concise and precise definition.
My question is : what would be a definition of such a family of theorems ?
And a second question along : is this min-max theorem concept always linked to the strong duality theorem, meaning that they mainly state that one problem is actually the dual of the other, like the max-flow-min-cut is ?