Infinite paths and cliques in random graphs

Alessandro Berarducci, Pietro Majer, Matteo Novaga
2012 Fundamenta Mathematicae  
We study the thresholds for the emergence of various properties in random subgraphs of (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 is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.
doi:10.4064/fm216-2-6 fatcat:sevm7t2x3zg7nfivxdlmejv7li