# Infinite paths and cliques in random graphs

created by novaga on 16 Sep 2008
modified on 10 Nov 2018

[BibTeX]

Published Paper

Inserted: 16 sep 2008
Last Updated: 10 nov 2018

Journal: Fund. Math.
Volume: 216
Pages: 163-191
Year: 2012

Abstract:

We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made.

The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.