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A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring (Memoirs of the American Mathematical Society)
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Description for A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring (Memoirs of the American Mathematical Society)
Paperback. Presents generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting. Series: Memoirs of the American Mathematical Society. Num Pages: 66 pages, illustrations. BIC Classification: PBV. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 253 x 180 x 5. Weight in Grams: 162.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2005
Publisher
American Mathematical Society
Condition
New
Series
Memoirs of the American Mathematical Society
Number of Pages
66
Place of Publication
Providence, United States
ISBN
9780821838259
SKU
V9780821838259
Shipping Time
Usually ships in 5 to 9 working days
Ref
99-3
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