A vertex set D in a finite undirected graph G is an efficient dominating set (e.d.s. for short) of G if every vertex of G is dominated by exactly one vertex of D. The 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.

Supplementary data are available at Bioinformatics online.

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