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

Friedgut, Ehud; Rodl, Vojtech; Rucinski, Andrzej; Tetali, Prasad

Couverture souple

ISBN 10 : 0821838253 ISBN 13 : 9780821838259

Editeur : American Mathematical Society, 2005

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2005
• Langue: anglais
• ISBN 10: 0821838253
• ISBN 13: 9780821838259
• Reliure: Broché
• Nombre de pages: 66
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible