Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Tuesday, May 29, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Pascal Pfister

H-bootstrap percolation

Let H be a a fixed graph. H-bootstrap percolation is then defined as follows. We start with a set G \subseteq E(K_n) of initially "infected" edges. Afterwards, the process proceeds in rounds. At time t ≥ 1, an edge e becomes infected if there exists a copy of H in K_n for which all edges except e are infected at time t-1. We say that a graph G percolates in K_n if eventually all edges of E(K_n) are infected. We study this process in the setting where the initial graph G is a random graph G_{n,p} and H is the complete graph K_r. We determine the critical probability p_c(n,K_r) for K_r-bootstrap percolation up to a constant factor, therewith improving the currently best known bounds for p_c(n,K_r) and answering an open question posed by Balogh, Bollobàs and Morris.

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