On Dissemination Thresholds in Regular and Irregular Graph Classes

  • I. Rapaport
  • K. Suchan
  • I. Todinca
  • J. Verstraete
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)


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. 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.


Random Graph Regular Graph Graph Class Active Vertex Bootstrap Percolation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • I. Rapaport
    • 1
  • K. Suchan
    • 1
    • 2
  • I. Todinca
    • 3
  • J. Verstraete
    • 4
  1. 1.Departamento de Ingeniería Matemática and Centro de Modelamiento MatemáticoUniversidad de Chile 
  2. 2.Faculty of Applied MathematicsAGH - University of Science and TechnologyCracowPoland
  3. 3.LIFOUniversité d’OrléansFrance
  4. 4.University of CaliforniaSan DiegoUSA

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