## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1328-1335 |

Number of pages | 8 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 119 |

Issue number | 6 |

DOIs | |

State | Published - Aug 2012 |

## Keywords

- Bootstrap percolation
- Linear algebra
- Weak saturation

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics