Abstract

Let $\mathcal{𝒜},\mathcal{ℬ}\subset \left(\genfrac{}{}{0.0pt}{}{[n]}{3}\right)$ be nontrivial cross-intersecting $3$-graphs. That is, ${\bigcap <!--FUNCTION\; APPLICATION-->}_{A\in \mathcal{𝒜}}A=\varnothing ={\bigcap <!--FUNCTION\; APPLICATION-->}_{B\in \mathcal{ℬ}}B$ and $A\cap B\ne \varnothing$ for all $A\in \mathcal{𝒜}$, $B\in \mathcal{ℬ}$. The best possible upper bound $\left|\mathcal{𝒜}\right|\left|\mathcal{ℬ}\right|\le {(3n-8)}^2$ is established for $n\ge 6$.

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