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lucatrevisan.wordpress.com | ||
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anuragbishnoi.wordpress.com
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| | | | | The Ramsey number $latex R(s, t)$ is the smallest $latex n$ such that every graph on $latex \geq n$ vertices either contains a clique of size $latex s$ or an independent set of size $latex t$. Ramsey's theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has been a major challenge... | |
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www.jeremykun.com
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| | | | | For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$. | |
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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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www.dicebreaker.com
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| | | Board games. For everyone. | ||
