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Minimum number of edges in a hypergraph guaranteeing a perfect fractional matching and the MMS conjecture

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Abstract

In this paper we prove the Ahlswede-Khachatrian conjecture [1] up to a finite number of cases, which can be checked using modern computers. This conjecture implies the conjecture from [2] and the Manickam-Miklós-Singhi conjecture.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil

    V. M. Blinovsky

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  1. V. M. Blinovsky
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Correspondence to V. M. Blinovsky.

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Original Russian Text © V.M. Blinovsky, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 4, pp. 43–54.

Supported by the São Paulo Research Foundation (FAPESP), project nos. 2012/13341-8 and 2013/07699-0, and NUMEC/USP, Project MaCLinC-USP.

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Blinovsky, V.M. Minimum number of edges in a hypergraph guaranteeing a perfect fractional matching and the MMS conjecture. Probl Inf Transm 50, 340–349 (2014). https://doi.org/10.1134/S0032946014040048

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  • DOI: https://doi.org/10.1134/S0032946014040048

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