Safe Sets in Graphs: Graph Classes and Structural Parameters

@inproceedings{gueda2016SafeSI,
  title={Safe Sets in Graphs: Graph Classes and Structural Parameters},
  author={Raquel {\'A}gueda and Nathann Cohen and Shinya Fujita and Sylvain Legay and Yannis Manoussakis and Yasuko Matsui and Leandro Montero and Reza Naserasr and Yota Otachi and Tadashi Sakuma and Zsolt Tuza and Renyu Xu},
  booktitle={COCOA},
  year={2016}
}
A safe set of a graph \(G=(V,E)\) is a non-empty subset S of V such that for every component A of G[S] and every component B of \(G[V \setminus S]\), we have \(|A| \ge |B|\) whenever there exists an edge of G between A and B. In this paper, we show that a minimum safe set can be found in polynomial time for trees. We then further extend the result and present polynomial-time algorithms for graphs of bounded treewidth, and also for interval graphs. We also study the parameterized complexity of… CONTINUE READING

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