= Modular intersection graph
{title2=$N=4p-1,\quad k=2p-1,\quad A\sim B\Longleftrightarrow|A\cap B|=p-1$}
For a <prime number> $p$, the <vertices> are $k$-subsets of $[N]$. An <independent set> avoids the only off-diagonal intersection congruent to $k$ modulo $p$, so the <Frankl-Wilson theorem> bounds its size by $\binom N{p-1}$. A <clique> has constant intersection $p-1$ and has size at most $N$, by the same theorem modulo a prime larger than $k$. This explicit <graph> gives an asymmetric <Ramsey number> lower bound and an exponential <chromatic number> lower bound.
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