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www.jeremykun.com | ||
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yufeizhao.wordpress.com
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| | | | | Eyal Lubetzky and I just finished and uploaded to the arXiv our new paper On the variational problem for upper tails of triangle counts in sparse random graphs. This paper concerns the following question: The upper tail problem for triangles. What is the probability that the number of triangles in an Erd?s-Rényi graph graph $latex... | |
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jeremykun.wordpress.com
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| | | | | Define the Ramsey number $ R(k,m)$ to be the minimum number $ n$ of vertices required of the complete graph $ K_n$ so that for any two-coloring (red, blue) of the edges of $ K_n$ one of two things will happen: There is a red $ k$-clique; that is, a complete subgraph of $ k$... | |
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gowers.wordpress.com
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| | | | | Here is a simple but important fact about bipartite graphs. Let $latex G$ be a bipartite graph with (finite) vertex sets $latex X$ and $latex Y$ and edge density $latex \alpha$ (meaning that the number of edges is $latex \alpha |X||Y|$). Now choose $latex (x_1,x_2)$ uniformly at random from $latex X^2$ and $latex (y_1,y_2)$ uniformly | |
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runswiththedug.wordpress.com
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