The f-Critical Set problem is NP-complete on planar subcubic bipartite graphs with m(f)=2, W[1]-hard parameterized by treewidth alone, yet FPT parameterized by treewidth plus m(f) or Δ(G), with kernels of size O(k·m(f)) and O(k·Δ(G)).
Agur, Fixed points of majority rule cellular automata with application to plasticity and precision of the immune system, Complex Syst
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Parameterized complexity of the f-Critical Set problem
The f-Critical Set problem is NP-complete on planar subcubic bipartite graphs with m(f)=2, W[1]-hard parameterized by treewidth alone, yet FPT parameterized by treewidth plus m(f) or Δ(G), with kernels of size O(k·m(f)) and O(k·Δ(G)).