Bounded-size coalition formation is FPT for treewidth-plus-capacity and vertex cover, W[1]-hard for tree-depth alone, and admits a polynomial kernel only in the unweighted case.
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Exact Algorithms and Lower Bounds for Forming Coalitions of Constrained Maximum Size
Bounded-size coalition formation is FPT for treewidth-plus-capacity and vertex cover, W[1]-hard for tree-depth alone, and admits a polynomial kernel only in the unweighted case.