FPT algorithm counts minimum (S,T)-edge-cuts of size p in time 2^{O(p^2)} n^{O(1)} via a drainage transformation that isolates at most n successive min-cuts whose edges cover every min-cut.
, Saurabh, S.: Minimum bisection is fixed parameter tractable
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Fixed-parameter tractability of counting small minimum $(S,T)$-cuts
FPT algorithm counts minimum (S,T)-edge-cuts of size p in time 2^{O(p^2)} n^{O(1)} via a drainage transformation that isolates at most n successive min-cuts whose edges cover every min-cut.