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terrytao.wordpress.com | ||
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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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anuragbishnoi.wordpress.com
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| | | | | Finite geometry is often used to construct graphs with certain extremal properties. For example, the Norm graphs are one of the best-known constructions in extremal graph theory (see this for a geometrical description of these graphs). Similarly, generalized polygons, and their substructures, give various constructions in Ramsey theory, the degrtocee-diameter problem, and the (bipartite) forbidden... | |
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xenaproject.wordpress.com
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| | | | | (This is a guest post by Bhavik Mehta) On March 16, 2023, a paper by Campos, Griffiths, Morris, and Sahasrabudhe appeared on the arXiv, announcing an exponential improvement to the upper bound on Ramsey numbers, an open problem since 1935. Around the same time, posts by Terence Tao, Timothy Gowers and Gil Kalai appeared, all... | |
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jiggerwit.wordpress.com
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| | | YBC 7289 Introduction (A pdf version of this post appears at the end of this post.) We propose a one-shot calculation of ?2 using Babylonian mathematics. An Old-Babylonian (OB) tablet YBC 7289 (from around 1800 B.C. to 1600 B.C.) contains the approximation B = 1 + 24/60 + 51/602 + 10/603 = 30547/21600 for ?2.... | ||
