Finding Efficient Domination for P_8-Free Bipartite Graphs in Polynomial Time
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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 known to be -complete for P_7-free graphs, and even for very restricted H-free bipartite graph classes such as for K_1,4-free bipartite graphs as well as for C_4-free bipartite graphs while it is solvable in polynomial time for P_7-free bipartite graphs as well as for S_2,2,4-free bipartite graphs. Here we show that ED can be solved in polynomial time for P_8-free bipartite graphs.
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