#### Conference abstracts

Session B2 - Graph Theory and Combinatorics

July 13, 16:00 ~ 16:25 - Room B7

## Critical percolation on random regular graphs

### University of Birmingham, United Kingdom   -   g.perarnau@bham.ac.uk

We show that for all $d\in \{3,\ldots,n-1\}$ the size of the largest component of a random $d$-regular graph on $n$ vertices at the percolation threshold $p=1/(d-1)$ is $\Theta(n^{2/3})$, with high probability. This extends known results for fixed $d\geq 3$ and for $d=n-1$, confirming a prediction of Nachmias and Peres on a question of Benjamini. In contrast to previous approaches, our proof is based on an application of the switching method.

Joint work with Felix Joos (University of Birmingham).

FoCM 2017, based on a nodethirtythree design.