On dissemination thresholds in regular and irregular graph classes

Authors:
I. Rapaport;K. Suchan;I. Todinca;J. Verstraete
Affiliations:
Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile;Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile and Faculty of Applied Mathematics, AGH-University of Science and Technology, Craco ...;LIFO, Université d'Orléans, France;University of California, San Diego, California
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

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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. We show that in any cubic graph, with high probability, the information will not spread to all vertices in the graph if p p.