A vertex set $D$ in a finite undirected graph $G$ is an {\em efficient dominating set} (\emph{e.d.s.}\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.s.\ in $G$, is \NP-complete for various $H$-free bipartite graphs, e.g., Lu and Tang showed that ED is \NP-complete for chordal bipartite graphs and for planar bipartite graphs; actually, ED is \NP-complete even for planar bipartite graphs with vertex degree at most 3 and girth at least $g$ for every fixed $g$. Thus, ED is \NP-complete for $K_{1,4}$-free bipartite graphs and for $C_4$-free bipartite graphs. In this paper, we show that ED can be solved in polynomial time for $S_{1,3,3}$-free bipartite graphs.

翻译：在限定的无方向图形中设定的顶点为$D$,G$是一个有效的顶点设置 (\ emph{ e.d.s. ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ $G$) $G$ 如果每个G$的顶点完全由一个美元顶点支配的话,G$ 的顶点设置为$D美元。 eemph { fficist Domination} (ED) 问题要求每个固定的$G$存在e.d.s.\ g$。 因此,对于各种无H$$l+1. 4 双面图来说,NP= $NP- complete bipartite 图形和平面双面图来说,G$NP=NP=NP- comple $NP$;对于每个固定的 $G$G$。因此,ED=无面的双面图和 $_ 4$- free bipart listal plain plain 3,这张纸面图可以显示我们正解 $3 。