A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring - Brossura

Rodl, Vojtech; Rucinski, Andrzej

Brossura

ISBN 10: 0821838253 ISBN 13: 9780821838259

Casa editrice: Amer Mathematical Society, 2005

Riassunto

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 we establish a sharp threshold for random graphs with this property. Let $G(n,p)$ be the random graph on $n$ vertices with edge probability $p$. We 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 setting.

Su questo libro

Product Description

Book by Ehud Friedgut Vojtech Rdl Andrzej Rucinski and Pr

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0821838253
• ISBN 13: 9780821838259
• Rilegatura: Copertina flessibile
• Numero di pagine: 66
• Redattore: Friedgut Ehud
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile