On Dissemination Thresholds in Regular and Irregular Graph Classes

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 < 1 2 . We give families of graphs in which information spreads to all vertices with high probability for relatively small values of p.

• Type: Journal
• Year: 2011
• Where: ALGORITHMICA
• Authors: Ivan Rapaport, Karol Suchan, Ioan Todinca, Jacques Verstraëte
• Keywords: Active Vertices, ALGORITHMICA 2011, Artificial Intelligence, Information, Various Graph Classes