On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets

In a reconfiguration version of decision problem \(\mathcal {Q}\) the input is an instance and two feasible solutions S T. The objective to determine whether there exists step-by-step transformation between T such that all intermediate steps also constitute solutions. this work, we study parameterized complexity Connected Dominating Set Reconfiguration (CDS-R). It was shown in previous work (DS-R) by k, maximum allowed size dominating set sequence, fixed-parameter tractable on graphs exclude biclique \(K_{d,d}\) as subgraph, for some constant \(d \ge 1\). We show additional connectivity constraint makes much harder, namely, CDS-R W[1]-hard \(k+\ell \), plus length already 5-degenerate graphs. On positive side, k tractable, fact admits polynomial kernel planar