Abstract
Let G be a graph and Ds and Dt be two dominating sets of G of size k. Does there exist a sequence 〈D0=Ds,D1,…,Dℓ−1,Dℓ=Dt〉 of dominating sets of G such that Di+1 can be obtained from Di by replacing one vertex with one of its neighbors? In this paper, we investigate the complexity of this decision problem. We first prove that this problem is PSPACE-complete, even when restricted to split, bipartite or bounded treewidth graphs. On the other hand, we prove that it can be solved in polynomial time on dually chordal graphs (a superclass of both trees and interval graphs) or cographs.
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