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Conference Papers Year : 2016

Safe Sets in Graphs: Graph Classes and Structural Parameters

Abstract

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 \ S], we have |A| ≥ |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 the problem. We show that the problem is fixed-parameter tractable when parameterized by the solution size. Furthermore, we show that this parameter lies between tree-depth and vertex cover number.
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Dates and versions

hal-01624255 , version 1 (26-10-2017)

Identifiers

  • HAL Id : hal-01624255 , version 1

Cite

Nathann Cohen, Raquel Águeda, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, et al.. Safe Sets in Graphs: Graph Classes and Structural Parameters. COCOA 2016 - 10th International Conference Combinatorial Optimization and Applications, Dec 2016, Hong Kong, China. pp.241-253. ⟨hal-01624255⟩
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