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A note on the grid Ramsey problem. (arXiv:1709.09658v1 [math.CO])
来源于:arXiv
The grid Ramsey number $ G(r) $ is the smallest number $ n $ such that every
edge-colouring of the grid graph $\Gamma_{n,n} := K_n \times K_n$ with $r$
colours induces a rectangle whose parallel edges receive the same colour. We
show $ G(r) \leq r^{\binom{r+1}{2}} - \left( 1/4 - o(1) \right)
r^{\binom{r}{2}+1} $, slightly improving the currently best known upper bound
due to Gy\'arf\'as. 查看全文>>