Aspects of upper defensive alliances

Cristina Bazgan, Henning Fernau, Z. Tuza

Research output: Contribution to journalArticle


A defensive alliance in a graph G=(V,E) is a set of vertices S satisfying the condition that every vertex v∈S has at least as many neighbors (including itself) in S than it has in V∖S. We also consider strong defensive alliances where the vertex itself is not considered in the inequality. We consider two notions of minimality in this paper, local and global minimality and we are interested in minimal (strong) defensive alliances of maximum size. We also look at connected versions of these alliances. We show that these problems are NP-hard.

Original languageEnglish
JournalDiscrete Applied Mathematics
Publication statusAccepted/In press - Jan 1 2018



  • Approximability
  • Defensive alliance
  • Graphs of bounded average degree
  • NP-hardness

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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