Is there a way to show R2(s + 1, t + 1) > s · t ?
The only way I know finding ramsey numbers to by graphing. But to prove the above inequality, what would be the best method?
2026-03-28 15:46:11.1774712771
Is there a way to show R2(s + 1, t + 1) > s · t .
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Given a set of size $s\cdot t$, partition it into $s$ blocks of $t$ elements each. Then color the 2-element subsets by making a pair red if it's included in one block and blue otherwise.
For this coloring, any red-homogeneous set is included in a single block and therefore has at most $t$ elements. Any blue-homogeneous set has at most one element per block and therefore has at most $s$ elements.