Towards a hypergraph version of the Pósa-Seymour conjecture

Matías Pavez-Signé, Nicolás Sanhueza-Matamala, Maya Stein

We prove that for fixed $r\ge k\ge 2$, every $k$-uniform hypergraph on $n$ vertices having minimum codegree at least $(1-(\left(\genfrac{}{}{0ex}{}{r-1}{k-1}\right)+\left(\genfrac{}{}{0ex}{}{r-2}{k-2}\right){)}^{-1})n+o(n)$ contains t…