Algorithmica

, Volume 59, Issue 1, pp 16–34 | Cite as

On Dissemination Thresholds in Regular and Irregular Graph Classes

Open Access
Article

Abstract

We investigate the natural situation of the dissemination of information on various graph classes starting with a random set of informed vertices called active. Initially active vertices are chosen independently with probability p, and at any stage in the process, a vertex becomes active if the majority of its neighbours are active, and thereafter never changes its state. This process is a particular case of bootstrap percolation. We show that in any cubic graph, with high probability, the information will not spread to all vertices in the graph if \(p<\frac{1}{2}\) . We give families of graphs in which information spreads to all vertices with high probability for relatively small values of p.

Keywords

Bootstrap percolation Cubic graphs Information dissemination 

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • I. Rapaport
    • 1
  • K. Suchan
    • 2
    • 3
  • I. Todinca
    • 4
  • J. Verstraete
    • 5
  1. 1.Departamento de Ingeniería Matemática and Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile
  2. 2.Facultad de Ingeniería y CienciasUniversidad Adolfo IbañezSantiagoChile
  3. 3.Faculty of Applied MathematicsAGH–University of Science and TechnologyCracowPoland
  4. 4.LIFOUniversité d’OrléansOrléansFrance
  5. 5.University of CaliforniaSan DiegoUSA

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