Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 02, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Alexey Pokrovskiy (Birkbeck, University of London)

Slow graph Bootstrap percolation

Graph-bootstrap percolation, also known as weak saturation, was introduced by Bollobás. For a fixed graph H, the H-bootstrap percollation process is defined as follows. We start with initial graph of “infected” set of edges, and we infect new edges in a sequence of rounds. In every round, given a set of previously infected edges G, we infect each non-infected edge e if it completes a new copy of H in G. A question raised by Bollobás asks for the maximum number of rounds the process can run before it stabilizes (i.e. until it stops infecting new edges). In this talk we will consider this question for the Kr-bootstrap percolation process for r at least 5 and improve previous bounds on the problem. This is joint work with Balogh, Kronenberg, and Szabó.

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