Andrzej Rucinski

Adam Mickiewicz University in Polznan, Poland; Emory University

November 15, 2010

A perfect matching in a k-uniform hypergraph H = (V, E) on n vertices

is a set of n/k disjoint edges of H, while a fractional perfect matching

in H is a function w : E → [0, 1] such that for each v ∈ V we have

e∋v w(e) = 1. Given n ≥ 3 and 3 ≤ k ≤ n, let m be the smallest

integer such that whenever the minimum vertex degree in H satisfies

δ(H) ≥ m then H contains a perfect matching, and let m∗ be defined

analogously with respect to fractional perfect matchings. Clearly, m∗ ≤

m.

We prove that for large n, m ∼ m∗ , and suggest an approach to deter-

mine m∗ , and consequently m, utilizing the Farkas Lemma.

This is a joint work with Vojta Rodl.