Independence and Efficient Domination on P6-free Graphs

@article{Lokshtanov2016IndependenceAE,
  title={Independence and Efficient Domination on P6-free Graphs},
  author={D. Lokshtanov and Marcin Pilipczuk and E. J. V. Leeuwen},
  journal={ACM Transactions on Algorithms (TALG)},
  year={2016},
  volume={14},
  pages={1 - 30}
}
In the Maximum Weight Independent Set problem, the input is a graph G, every vertex has a non-negative integer weight, and the task is to find a set S of pairwise nonadjacent vertices, maximizing the total weight of the vertices in S. We give an nO(log2 n) time algorithm for this problem on graphs excluding the path P6 on 6 vertices as an induced subgraph. Currently, there is no constant k known for which Maximum Weight Independent Set on Pk-free graphs becomes NP-hard, and our result implies… Expand
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