Georgia Institute of Technology College of Sciences

A perfect matching in a $k$-uniform hypergraph $H=(V,E)$ on $n$ vertices is a set of$n/k$ disjoint edges of $H$, whilea fractional perfect matching in $H$ is a function $w:E --> [0,1]$ such that for each $v\in V$ we have $\sum_{e\ni v} w(e) = 1.$ Given $n \ge 3$ and $3\le k\le n$, let $m$ be the smallest integer suchthat whenever the minimum vertex degree in $H$ satisfies $\delta(H)\ge m$ then $H$ contains aperfect matching, and let $m^*$ be defined analogously with respect to fractional perfectmatchings. Clearly, $m^*\le m$.We prove that for large $n$, $m\sim m^*$, and suggest an approach to determine $m^*$, andconsequently $m$, utilizing the Farkas Lemma. This is a joint work with Vojta Rodl.