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Article Dans Une Revue Information Processing Letters Année : 2014

Strict Majority Bootstrap Percolation in the r-wheel

Guillaume Theyssier
Kiwi Marcos
  • Fonction : Auteur
Rapaport Ivan
  • Fonction : Auteur
Rica Sergio
  • Fonction : Auteur
Espanés Pablo Moisset De
  • Fonction : Auteur

Résumé

In the strict Majority Bootstrap Percolation process each passive vertex v becomes active if at least View the MathML source⌈deg(v)+12⌉ of its neighbors are active (and thereafter never changes its state). We address the problem of finding graphs for which a small proportion of initial active vertices is likely to eventually make all vertices active. We study the problem on a ring of n vertices augmented with a "central" vertex u. Each vertex in the ring, besides being connected to u, is connected to its r closest neighbors to the left and to the right. We prove that if vertices are initially active with probability p>1/4p>1/4 then, for large values of r, percolation occurs with probability arbitrarily close to 1 as n→∞n→∞. Also, if p<1/4p<1/4, then the probability of percolation is bounded away from 1.

Dates et versions

hal-00943800 , version 1 (08-02-2014)

Identifiants

Citer

Guillaume Theyssier, Kiwi Marcos, Rapaport Ivan, Rica Sergio, Espanés Pablo Moisset De. Strict Majority Bootstrap Percolation in the r-wheel. Information Processing Letters, 2014, pp.Volume 114, Issue 6, June 2014, Pages 277-281. ⟨10.1016/j.ipl.2014.01.005⟩. ⟨hal-00943800⟩
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