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

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.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login