FPT under feedback edge set parameterization

Determine whether the s-Club Cluster Edge Deletion problem is fixed-parameter tractable when parameterized by the feedback edge set number of the input graph; namely, decide if there exists an algorithm running in time f(fe(G))·n^{O(1)} for arbitrary s ≥ 1.

Background

Beyond the parameters treated in the paper (neighborhood diversity, twin cover, cluster vertex deletion) and those shown hard (pathwidth, treewidth), the authors explicitly single out the feedback edge set as an open parameterization.

They suggest that resolving whether s-Club Cluster Edge Deletion is FPT under feedback edge set would further complete the structural parameterization picture for the problem.