On Dissemination Thresholds in Regular and Irregular Graph Classes

  • Authors:

  • I. Rapaport;K. Suchan;I. Todinca;J. Verstraete

  • Affiliations:

  • Universidad de Chile, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Santiago, Chile;Universidad Adolfo Ibañez, Facultad de Ingeniería y Ciencias, Santiago, Chile and AGH–University of Science and Technology, Faculty of Applied Mathematics, Cracow, Poland;Université d’Orléans, LIFO, Orléans, France;University of California, San Diego, CA, USA

  • Venue:
  • Algorithmica - Special Issue: Latin American Theoretical Informatics
  • Year:
  • 2011

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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 $pp.