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Item Details
| Title:
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A SHARP THRESHOLD FOR RANDOM GRAPHS WITH A MONOCHROMATIC TRIANGLE IN EVERY EDGE COLORING
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| By: |
Ehud Friedgut, Vojtech Rodl, Andrzej Rucinski |
| Format: |
Paperback |
| List price:
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£55.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821838253 |
| ISBN 13: |
9780821838259 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 December, 2005 |
| Edition: |
Illustrated edition |
| Series: |
Memoirs of the American Mathematical Society No. 179 |
| Pages: |
66 |
| Description: |
Presents generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting. |
| 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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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