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.