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Combinatorics: Sahar Diskin (TAU) | Einstein Institute of Mathematics

Combinatorics: Sahar Diskin (TAU)

Date: 
Mon, 02/05/202211:00-13:00
Location: 
Sprinzak 202

HUJI Combinatorics Seminar 


When: Monday May 2nd, 2022, at 11AM (Israel time)
Where: Sprinzak 202


Speaker: Sahar Diskin (TAU)


Title: Supercritical Site Percolation on the Hypercube: Small components are small
Abstract:
In the site percolation model, a random induced subgraph G[R] of a given graph G is formed by putting every vertex v of G into a random subset R with probability p and independently. One then researches typical properties of G[R], like the sizes of its connected components.
In this talk, we consider supercritical site percolation on the d-dimensional hypercube Q^d. We show that typically all components in the percolated hypercube, besides the giant, are of size O(d). This resolves a conjecture of Bollobás, Kohayakawa, and Łuczak from 1994.
Joint work with Michael Krivelevich.