A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring is popular PDF and ePub book, written by Ehud Friedgut in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring can be Read Online from any device for your convenience.
A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring Book PDF Summary
Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper the authors establish a sharp threshold for random graphs with this property. Let $G(n, p)$ be the random graph on $n$ vertices with edge probability $p$. The authors prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n, (1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[ G(n, (1]\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1.$. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setti
Detail Book of A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring PDF
- Author : Ehud Friedgut
- Release : 19 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821838259
- Genre : Mathematics
- Total Page : 80 pages
- Language : English
- PDF File Size : 16,8 Mb
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