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The \\emph{Dominating Induced Matching} (\\emph{DIM}) problem asks for the existence of a d.i.m.\\ in $G$. The DIM problem is \\NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but was solved in linear time for $P_7$-free graphs and in polynomial time for $P_8$-free graphs. 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