Minimal Number of Edges in Hypergraph Guaranteeing Perfect Fractional Matching and MMS Conjecture

Abstract

We prove Ahlswede- Khachatrian conjecture. From this conjecture follows of several other conjectures including Manickam-Miklós-Singhi conjecture.

final version

References in corpus (2)

• On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands
• A linear bound on the Manickam-Miklos-Singhi Conjecture

Cited by in corpus (6)

• A Note on the Manickam-Miklós-Singhi Conjecture for Vector Spaces
• A New Quadratic Bound for the Manickam-Miklós-Singhi Conjecture
• Fractional matching in hypergraphs
• The Manickam-Miklós-Singhi Conjectures for Sets and Vector Spaces
• Comments to Symmetrical Smoothing Method and First Step to How to Avoid Irrelevant Extremums
• Erdös's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method