The power of small coalitions in graphs

  • Authors:

  • J.-C. Bermond;J. Bond;D. Peleg;S. Perennes

  • Affiliations:

  • I3S CNRS, Univ. de Nice-Sophia Antipolis and INRIA project MASCOTTE, 2004 Route des Lucioles, BP 93, F-06902 Sophia-Antipolis , France;I3S CNRS, Univ. de Nice-Sophia Antipolis, France;Department of Applied Mathematics and Computer Science, Faculty of Mathematical Science, The Weizmann Institute, P.O. Box 26, Rehovot 76100, Israel;I3S CNRS, Univ. de Nice-Sophia Antipolis and INRIA project MASCOTTE, 2004 Route des Lucioles, BP 93, F-06902 Sophia-Antipolis , France

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2003

Quantified Score

Hi-index 0.05

Visualization

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 general graph. Say that a vertex v is controlled by the coalition M if the majority of its neighbors are from M. We ask how many vertices (as a function of |M|) can M control in this fashion. Upper and lower bounds are provided for this problem, as well as for cases where the majority is computed over larger neighborhoods (either neighborhoods of some fixed radius r ≥ 1, or all neighborhoods of radii up to r). In particular, we look also at the case where the coalition must control all vertices (including or excluding its own), and derive bounds for its size.