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 motivated by parallel resource allocation problems,encoding theory and network routing. It is NP-complete even for veryrestricted graph classes such as planar bipartite graphs with maximum degree 3and is solvable in linear time for $P_7$-free graphs, and in polynomial timefor $S_{1,2,4}$-free graphs as well as for $S_{2,2,2}$-free graphs. In thispaper, combining two distinct approaches, we solve it in polynomial time for$S_{2,2,3}$-free graphs.
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机译：让$ g =（v，e）$是有限的无向图。 Edge Set $ E' Subseteq E $是$ G $的{ em d.i.m.}），如果每一个边缘以$ e'$的恰好始终为$ e $。 emph {占主导地匹配}（ emph {dim}）问题要求存在d.i.m. 以$ g $;这个问题也称为 emph {高效的边缘统治}问题;线图是有效的统治问题。暗淡问题是通过并行资源分配问题，编码理论和网络路由的激励。即使对于稳定的图形类（如诸如最大程度的平面图形图），它也是 np-specting，以$ p_7 $ -free图表中的线性时间和$ s_ {1,2,4} $ - 免费图形是可靠的以及$ S_ {2,2,2} $ - 免费图形。在此纸纸中，组合两个不同的方法，我们在多项式时间内解决$ S_ {2,2,3} $ - 免费图形。
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