2 problems

Let $P_n$ be the path on $n$ vertices, let $P_n\mathbin{\square}P_n$ be the $n\times n$ Cartesian grid, and let $\operatorname{gp}_f$ denote the fractional general position number.…

Let $G$ be an $r$-graph. A $(t,r)$-PM is a multiset of $t\cdot r$ perfect matchings of $G$ such that every edge of $G$ is contained in exactly $t$ of them. The per-degree fractiona…