Lower bounds for graph bootstrap percolation via properties of polynomials
Combinatorics
2021-05-11 v2
Abstract
We introduce a simple method for proving lower bounds for the size of the smallest percolating set in a certain graph bootstrap process. We apply this method to determine the sizes of the smallest percolating sets in multidimensional tori and multidimensional grids (in particular hypercubes). The former answers a question of Morrison and Noel, and the latter provides an alternative and simpler proof for one of their main results.
Keywords
Cite
@article{arxiv.1708.04640,
title = {Lower bounds for graph bootstrap percolation via properties of polynomials},
author = {Lianna Hambardzumyan and Hamed Hatami and Yingjie Qian},
journal= {arXiv preprint arXiv:1708.04640},
year = {2021}
}