기초과학연구원 이산수학그룹
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A common technique to characterize hereditary graph classes is to exhibit their minimal obstructions. Sometimes, the set of minimal obstructions might be infinite, or too complicated to describe. For instance, for any $k\ge 3$, the set of minimal obstructions of the class of $k$-colourable graphs is yet unknown. Nonetheless, the Roy-Gallai-Hasse-Vitaver Theorem asserts that a graph $G$ … |
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A well-known conjecture of Burr and Erdős asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that $r(Q_n)=O(2^{2n−cn})$ for a universal constant $c>0$, improving upon the previous best-known bound $r(Q_n)=O(2^{2n})$, due to Conlon, Fox, and Sudakov. |
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