Gomory-Hu Tree

Why it matters

Gomory-Hu compactly encodes all min-cuts. Understanding shapes structural graph theory.

The architecture

Build tree T from n-1 max-flows.

Min-cut(u, v) = min edge on T path from u to v.

How it works end to end

Iterative: pair vertices; run max-flow; refine tree.

Uses Ford-Fulkerson variant.

Cut function submodular structure.