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yufeizhao.wordpress.com | ||
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dominiczypen.wordpress.com
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| | | | | Suppose you want to have a graph $latex G = (V,E)$ with chromatic number $latex \chi(G)$ equaling some value $latex k$, such that $latex G$ is minimal with this property. So you end up with a $latex k$-(vertex-)critical graph. It is easy to construct critical graphs by starting with some easy-to-verify example like $latex C_5$... | |
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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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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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lucatrevisan.wordpress.com
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| | | (This is the sixth in a series of posts on online optimization techniques and their ``applications'' to complexity theory, combinatorics and pseudorandomness. The plan for this series of posts is to alternate one post explaining a result from the theory of online convex optimization and one post explaining an ``application.'' The first two posts were... | ||
