Infinite paths and cliques in random graphs

A. Berarducci, P. Majer, M. Novaga

Published 2008-09-13, updated 2011-03-27Version 5

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.