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Let $G=(V,E)$ be a finite undirected graph. An edge set $E' \subseteq E$ is a{\em dominating induced matching} ({\em d.i.m.}) in $G$ if every edge in $E$ isintersected by exactly one edge of $E'$. The \emph{Dominating Induced Matching}(\emph{DIM}) problem asks for the existence of a d.i.m.\ in $G$; this problemis also known as the \emph{Efficient Edge Domination} problem; it is theEfficient Domination problem for line graphs.  The DIM problem is \NP-complete even for very restricted graph classes suchas planar bipartite graphs with maximum degree 3 and is solvable in linear timefor $P_7$-free graphs, and in polynomial time for $S_{1,2,4}$-free graphs aswell as for $S_{2,2,2}$-free graphs. In this paper, combining two distinctapproaches, we solve it in polynomial time for $S_{2,2,3}$-free graphs.

Finding Dominating Induced Matchings in $(S_{2,2,3})$-Free Graphs in Polynomial Time