105 citations
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math.CO2009★ 2 cited
The structure of almost all graphs in a hereditary property
Noga Alon, Jozsef Balogh, Bela Bollobas +1
A hereditary property of graphs is a collection of graphs which is closed under taking induced subgraphs. The speed of ¶is the function n \mapsto |¶_n|, where ¶_n denotes the graph…
math.CO2008★ 105 cited
Bootstrap percolation in three dimensions
József Balogh, Béla Bollobás, Robert Morris
By bootstrap percolation we mean the following deterministic process on a graph . Given a set of vertices "infected" at time 0, new vertices are subsequently infected, at ea…