Dominating Set Reconfiguration under token sliding is W[2]-hard on graphs of bounded treewidth and pathwidth, and its directed version is NP-hard on shallow DAGs, marking the first known separation from independent-set reconfiguration.
17 Marcin Wrochna
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Lower bounds for dominating set reconfiguration on sparse (directed) graphs
Dominating Set Reconfiguration under token sliding is W[2]-hard on graphs of bounded treewidth and pathwidth, and its directed version is NP-hard on shallow DAGs, marking the first known separation from independent-set reconfiguration.