Linear algebra and bootstrap percolation
In H-bootstrap percolation, a set A⊂V(H) of initially 'infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph H. A particular case of this is the H-bootstrap process, in which H encodes copies of H in a graph G. We find the minimum size of a set A that leads to complete infection when G and H are powers of complete graphs and H encodes induced copies of H in G. The proof uses linear algebra, a technique that is new in bootstrap percolation, although standard in the study of weakly saturated graphs, which are equivalent to (edge) H-bootstrap percolation on a complete graph. © 2012 Elsevier Inc.
Journal of Combinatorial Theory. Series A
Balogh, J., Bollobás, B., Morris, R., & Riordan, O. (2012). Linear algebra and bootstrap percolation. Journal of Combinatorial Theory. Series A, 119 (6), 1328-1335. https://doi.org/10.1016/j.jcta.2012.03.005