$d$-cluster-free sets with a given matching number

Xizhi Liu

Let $3\le d\le k$ and $\nu \ge 0$ be fixed and $\mathcal{F}\subset \left(\genfrac{}{}{0ex}{}{[n]}{k}\right)$. The matching number of $\mathcal{F}$, denoted by $\nu (\mathcal{F})$, is the maximum number of pairwise…