[PDF.21ee] A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring (Memoirs of the American Mathematical Society)

A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring (Memoirs of the American Mathematical Society)

[PDF.oq77] A Sharp Threshold for Random Graphs With a Monochromatic Triangle in Every Edge Coloring (Memoirs of the American Mathematical Society)

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 | #14853060 in Books |  American Mathematical Society |  2005-12-01 | Original language:English |  9.75 x7.00 x.25l,.36 | File type: PDF | 66 pages

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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-...

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