Parameterized Complexity in Multiple-Interval Graphs: Domination

We show that several variants of the problem k-Dominating Set, including k-Connected Dominating Set, k-Independent Dominating Set, k-Dominating Clique, d-Distancek-Dominating Set, k-Perfect Code and d-Distancek-Perfect Code, when parameterized by the solution size k, remain W[1]-hard in either multiple-interval graphs or their complements or both.