Abstract
Ramsey’s theorem implies that for all graphs F and r we have \(K_{n} \rightarrow (F)_{r}^{e}\), for n large enough. At first sight it is not immediately clear whether this follows from the density of K n or its rich structure. As it turns out, studying Ramsey properties of random graphs shows that the later is the case, as random graphs give examples of sparse graphs with the desired Ramsey property.
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Prömel, H.J. (2013). Ramsey Statements for Random Graphs. In: Ramsey Theory for Discrete Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-01315-2_15
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DOI: https://doi.org/10.1007/978-3-319-01315-2_15
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