Immunity against local influence

Research output: Contribution to journalArticlepeer-review

Abstract

This paper considers the question of the influence of a coalition of vertices, seeking to gain control (or majority) in local neighborhoods in a graph. A vertex u is said to be controlled by the coalition M if the majority of its neighbors are from M. Let Ruled(G, M) denote the set of vertices controlled by M in G. Previous studies focused on constructions allowing small coalitions to control many vertices, and provided tight bounds for the maximum possible size of Ruled(G, M) (as a function of |M |). This paper introduces the dual problem, concerning the existence and construction of graphs immune to the influence of small coalitions, i.e., graphs G for which Ruled(G, M) is small (relative to |M| again) for every coalition M. Upper and lower bounds are derived on the extent to which such immunity can be achieved.

Original languageEnglish
Pages (from-to)168-179
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8001
DOIs
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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