A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring (Paperback, illustrated Edition)

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

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	Memoirs of the American Mathematical Society
Release date:	December 2005
Authors:	Ehud Friedgut • Vojtech Rodl • Andrzej Rucinski • Prasad Tetali
Dimensions:	253 x 180 x 5mm (L x W x T)
Format:	Paperback
Pages:	66
Edition:	illustrated Edition
ISBN-13:	978-0-8218-3825-9
Categories:	Books
LSN:	0-8218-3825-3
Barcode:	9780821838259

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