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A sharp threshold for random graphs with a monochromatic triangle in every edge coloring.


A sharp threshold for random graphs with a monochromatic triangle in every edge coloring.

Ed. by Ehud Friedgut et al.

Amer. Mathematical Society


66 pages



Memoirs of the American Mathematical Society; no.845


The authors propose the R is 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 they establish a sharp threshold for random graphs with this property. They examine the concept and its implications in full, determining that 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. They provide an outline of the proof, tepees and constellations, regularity, the core section (proof of Lemma 2.4), random graphs, a summary and a glossary.

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Publication:SciTech Book News
Article Type:Book review
Date:Mar 1, 2007
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