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11011110.github.io | ||
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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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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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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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cosmiaineurope.wordpress.com
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| | | Cosmia's travel in Europe from June 2018 to July 2018 | ||
