Combinatorial Methods in Bootstrap Percolation Problems

An elegant bootstrap percolation result on the hyperrectangle graph was proved by Balogh, Bollobás, Morris, and Riordan using a linear algebric method in 2012. This paper studies the same problem by purely combinatorial means. The base case is solved for all dimensions, and we pose open problems for the remaining cases.

Publication Details

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ArXiv.org
Published
2025-08-15
Primary Topic
Water Quality and Resources Studies
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article
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article

Combinatorial Methods in Bootstrap Percolation Problems

ArXiv.org
Water Quality and Resources Studies
article

Combinatorial Methods in Bootstrap Percolation Problems

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Abstract

An elegant bootstrap percolation result on the hyperrectangle graph was proved by Balogh, Bollobás, Morris, and Riordan using a linear algebric method in 2012. This paper studies the same problem by purely combinatorial means. The base case is solved for all dimensions, and we pose open problems for the remaining cases.

ArXiv.org
Openalex Percentile: Top 55%
Water Quality and Resources Studies
Open Access PDFOpenAlex
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Combinatorial Methods in Bootstrap Percolation Problems · ArXiv.org (2025) | TGRS Research Map | TGRS