6 problems

Lopsided fractional Erdős matching conjecture. For every $k$-graph $F$ and $0\leq\beta\leq 1/v(F)$,

For $k,\ell\in\mathbb N$ with $\ell\leq k-1$, let $c^*_{k,\ell}$ be the smallest number $c$ such that every $k$-graph $H$ on $n$ vertices with … contains a perfect fractional match…

Let $k\geq 3$ and let $G$ be a $k$-critical graph. Let $\mu(G)$ denote the matching number and $\mu_f(G)$ the fractional matching number. Fractional matching gap conjecture. If $G$…

Fractional Erdős matching conjecture. For integers $\ell,d\geq1$,

Let $H(n,k)=([n],E)$ be a $k$-uniform hypergraph, where $[n]=\{1,\ldots,n\}$, and let a perfect fractional matching be a collection of nonnegative real numbers…

Let $f_d(k,n)$ denote the minimum $d$-degree forcing a fractional matching of the relevant size in a $k$-uniform hypergraph, with $1\le d\le k-1$. Fractional matching threshold con…