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Title:
Fractional Perfect Matchings in Hypergraphs
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Abstract:
A perfect matching in a k-uniform hypergraph H = (V, E) on n verticesis a set of n/k disjoint edges of H, while a fractional perfect matchingin H is a function w : E → [0, 1] such that for each v ∈ V we havee∋v w(e) = 1. Given n ≥ 3 and 3 ≤ k ≤ n, let m be the smallestinteger such that whenever the minimum vertex degree in H satisfiesδ(H) ≥ m then H contains a perfect matching, and let m∗ be definedanalogously 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.
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