Safe Sets in Graphs: Graph Classes and Structural Parameters

  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},
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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Publications referenced by this paper.

Network Majority on Tree Topological Network

  • Electronic Notes in Discrete Mathematics
  • 2016

Bodlaender , Jitender S . Deogun , Klaus Jansen , Ton Kloks , Dieter Kratsch , Haiko Müller , and Zsolt Tuza . Rankings of graphs

L. Hans
  • SIAM J . Discrete Math
  • 1998

Bodlaender . A linear - time algorithm for finding tree - decompositions of small treewidth

L Hans
  • SIAM J . Comput
  • 1996

Treewidth, Computations and Approximations

  • Lecture Notes in Computer Science
  • 1994

Bodlaender . On linear time minor tests with depth - first search

L Hans
  • 1993