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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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| | 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$ vertices for which all edges are red. There is a blue $ m$-clique. It is known that these numbers are always finite, but it is very difficult to compute them exactly.
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| | Ben Gunby's new paper determining the large deviation rate for sparse random regular graphs.
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| My previous post was written with the help of a few very useful tools: LaTeX mathematical typesetting Gummi LaTeX editor Python programming language PyX Python / LaTeX graphics package my own PyPyX wrapper around PyX LaTeX2WP script for easy conversion from LaTeX to WordPress HTML