New Polynomial Case for Efficient Domination in P 6-free Graphs
نویسنده
چکیده
In a graph G, an efficient dominating set is a subset D of vertices such that D is an independent set and each vertex outside D has exactly one neighbor in D. The Efficient Dominating Set problem (EDS) asks for the existence of an efficient dominating set in a given graph G. The EDS is known to be NP -complete for P7-free graphs, and is known to be polynomial time solvable for P5-free graphs. However, the computational complexity of the EDS problem is unknown for P6free graphs. In this paper, we show that the EDS problem can be solved in polynomial time for a subclass of P6-free graphs, namely (P6, banner)free graphs.
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