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

On Dissemination Thresholds in Regular and Irregular Graph Classes

Open Access


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.


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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