Infinite paths and cliques in random graphs

Details Infinite paths and cliques in random graphs Infinite paths and cliques in random graphs

2008-09-13

arxiv.org/abs/0809.2335v5

Mathematics

Probability

18 pages

Scientific paper

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.

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