FPT under modular width parameterization

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

Background

Alongside other structural parameters, the authors highlight modular width as an unresolved case in their parameterized complexity landscape.

They provide FPT algorithms for neighborhood diversity, twin cover, and cluster vertex deletion, but do not settle whether modular width similarly yields an FPT algorithm for s-Club Cluster Edge Deletion.