Connectivity-preserving important separators of size at most k number 2^{O(k log k)} and can be enumerated in the same bound, yielding 2^{O(k log k)} FPT time for constant-class Node Multiway Cut-Uncut.
Disjoint paths and connected subgraphs for H-free graphs.Theoretical Computer Sci- ence, 898:59–68, 2022
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Connectivity-Preserving Important Separators: A Framework for Cut-Uncut Problems
Connectivity-preserving important separators of size at most k number 2^{O(k log k)} and can be enumerated in the same bound, yielding 2^{O(k log k)} FPT time for constant-class Node Multiway Cut-Uncut.