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11011110.github.io | ||
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yufeizhao.wordpress.com
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| | | | | This post is adapted from my new expository survey Extremal regular graphs: independent sets and graph homomorphisms. The earliest result in extremal graph theory is usually credited to Mantel, who proved, in 1907, that a graph on $latex {n}$ vertices with no triangles contains at most $latex {n^2/4}$ edges, where the maximum is achieved for... | |
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yufeizhao.com
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| | | | | Resolution of Kahn's conjecture on the maximum number of independent sets in a graph with prescribed degree-degree distributions. | |
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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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jeremykun.com
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| | | Hard to believe Sanjeev Arora and his coauthors consider it"a basic tool [that should be] taught to all algorithms students together with divide-and-conquer, dynamic programming, and random sampling."Christos Papadimitriou calls it"so hard to believe that it has been discovered five times and forgotten." It has formed the basis of algorithms inmachine learning, optimization, game theory, | ||
