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Linear algebra and bootstrap percolation

Abstract:

In $\HH$-bootstrap percolation, a set $A \subset V(\HH)$ of initially 'infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\HH$. A particular case of this is the $H$-bootstrap process, in which $\HH$ 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 $\HH$ encodes induced copies of $H$ in $G$. The proof uses linear algebra...

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Publication status:
Published

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Publisher copy:
10.1016/j.jcta.2012.03.005

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Journal:
JOURNAL OF COMBINATORIAL THEORY SERIES A
Volume:
119
Issue:
6
Pages:
1328-1335
Publication date:
2011-07-07
DOI:
EISSN:
1096-0899
ISSN:
0097-3165
URN:
uuid:7238c5aa-b2e8-4f72-a37d-7d91435acfc5
Source identifiers:
164004
Local pid:
pubs:164004
Language:
English
Keywords:

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