Finding Efficient Domination for S_1,1,5-Free Bipartite Graphs in Polynomial Time

10/29/2020

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by   Andreas Brandstädt, et al.

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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 -complete for various H-free bipartite graphs, e.g., Lu and Tang showed that ED is -complete for chordal bipartite graphs and for planar bipartite graphs; actually, ED is -complete even for planar bipartite graphs with vertex degree at most 3 and girth at least g for every fixed g. Thus, ED is -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_1,1,5-free bipartite graphs.