Site Percolation on PseudoRandom Graphs
Abstract
We consider vertex percolation on pseudorandom $d$regular graphs. The previous study by the second author established the existence of phase transition from small components to a linear (in $\frac{n}{d}$) sized component, at $p=\frac{1}{d}$. In the supercritical regime, our main result recovers the sharp asymptotic of the size of the largest component, and shows that all other components are typically much smaller. Furthermore, we consider other typical properties of the largest component such as the number of edges, existence of a long cycle and expansion. In the subcritical regime, we strengthen the upper bound on the likely component size.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.13326
 Bibcode:
 2021arXiv210713326D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Probability;
 05C80;
 60K35;
 82B43