Ramsey Statements for Random Graphs

Hans Jürgen Prömel
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Hans Jürgen Prömel: Technische Universität Darmstadt

Chapter Chapter 15 in Ramsey Theory for Discrete Structures, 2013, pp 171-183 from Springer

Abstract: 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.

Keywords: Random Graph; Ramsey Statements; Ramsey Property; Monochromatic Copy; Regular Copy (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-319-01315-2_15

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