Safe sets in graphs: Graph classes and structural parameters

Raquel Águeda, Nathann Cohen, Shinya Fujita, Sylvain Legay, Yannis Manoussakis, Yasuko Matsui, Leandro Montero, Reza Naserasr, Yota Otachi, Tadashi Sakuma, Z. Tuza, Renyu Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings
PublisherSpringer Verlag
Pages241-253
Number of pages13
Volume10043 LNCS
ISBN (Print)9783319487489
DOIs
Publication statusPublished - 2016
Event10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016 - Hong Kong, China
Duration: Dec 16 2016Dec 18 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10043 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016
CountryChina
CityHong Kong
Period12/16/1612/18/16

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Keywords

  • Fixed-parameter tractability
  • Graph algorithm
  • Interval graph
  • Safe set
  • Treewidth

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Águeda, R., Cohen, N., Fujita, S., Legay, S., Manoussakis, Y., Matsui, Y., Montero, L., Naserasr, R., Otachi, Y., Sakuma, T., Tuza, Z., & Xu, R. (2016). Safe sets in graphs: Graph classes and structural parameters. In Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings (Vol. 10043 LNCS, pp. 241-253). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10043 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-48749-6_18