Threshold behavior of bootstrap percolation.

Ahad N. Zehmakan

doi:10.1016/J.DISC.2020.112211

Threshold behavior of bootstrap percolation.

Ahad N. Zehmakan

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Consider a graph G and an initial random configuration, where each node is black with
probability p and white otherwise, independently. In discrete-time rounds, each node
becomes black if it has at least r black neighbors and white otherwise. We prove that
this basic process exhibits a threshold behavior with two phase transitions when the
underlying graph is a d-dimensional torus and identify the threshold values

Original language	English
Number of pages	14
Journal	Discret. Math.
Volume	344
Issue number	2
DOIs	https://doi.org/10.1016/J.DISC.2020.112211
Publication status	Published - Jan 2021
Externally published	Yes

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https://dblp.org/rec/journals/dm/Zehmakan21

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abstract = "Consider a graph G and an initial random configuration, where each node is black withprobability p and white otherwise, independently. In discrete-time rounds, each nodebecomes black if it has at least r black neighbors and white otherwise. We prove thatthis basic process exhibits a threshold behavior with two phase transitions when theunderlying graph is a d-dimensional torus and identify the threshold values",

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N2 - Consider a graph G and an initial random configuration, where each node is black withprobability p and white otherwise, independently. In discrete-time rounds, each nodebecomes black if it has at least r black neighbors and white otherwise. We prove thatthis basic process exhibits a threshold behavior with two phase transitions when theunderlying graph is a d-dimensional torus and identify the threshold values

AB - Consider a graph G and an initial random configuration, where each node is black withprobability p and white otherwise, independently. In discrete-time rounds, each nodebecomes black if it has at least r black neighbors and white otherwise. We prove thatthis basic process exhibits a threshold behavior with two phase transitions when theunderlying graph is a d-dimensional torus and identify the threshold values

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DO - 10.1016/J.DISC.2020.112211

M3 - Article

VL - 344

JO - Discret. Math.

JF - Discret. Math.

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ER -

Threshold behavior of bootstrap percolation.

Abstract

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