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arXiv · 2605.22708

The Manickam-Mikl\'os-Singhi Property in Graphs and Hypergraphs

Adam Džavoronok
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Abstract

This paper studies the Manickam-Mikl\'os-Singhi (MMS) property for graphs and hypergraphs. Using the structural characterisation of the $2$-uniform case, we construct new families of regular graphs with the MMS property. We then analyse the Erd\H{o}s--R\'enyi random graph model $\mathbf{G}(n,p)$ and identify regimes in which the MMS property holds with high probability. Finally, we extend the matching-based sufficient condition to higher uniformities via pseudo-matchings and introduce a blowout construction that produces higher-uniformity hypergraphs with the MMS property from lower-uniformity examples.

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Adam Džavoronok. 2026-05-21. The Manickam-Mikl\'os-Singhi Property in Graphs and Hypergraphs. https://arxiv.org/abs/2605.22708

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