Connectivity-preserving important separators can be enumerated in 2^{O(k log k)} time, yielding an FPT algorithm for Node Multiway Cut–Uncut that improves the previous 2^{O(k^2 log k)} dependence.
Connectivity-preserving minimum separator in at-free graphs
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Connectivity-Preserving Important Separators: A Framework for Cut-Uncut Problems
Connectivity-preserving important separators can be enumerated in 2^{O(k log k)} time, yielding an FPT algorithm for Node Multiway Cut–Uncut that improves the previous 2^{O(k^2 log k)} dependence.