A Note on Small Percolating Sets on Hypercubes via Generative AI

Bootstrap percolation, introduced by Chalupa, Leath, and Reich in their 1979 work [4], serves as a simplified model for ferromagnetic dynamics. Since then, it has been applied in numerous fields of physics and has become a significant topic of interest in mathematics. The process starts with an initial set of "infected" vertices in a graph G, where at each step, any vertex with at least r infected neighbors also becomes infected. A key problem in this framework is determining the minimum size of an initial set that results in the entire graph becoming infected, known as the percolating set. This minimum is denoted by m(G, r).