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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.22708 |
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| _version_ | 1866918530962685952 |
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| author | Džavoronok, Adam |
| author_facet | Džavoronok, Adam |
| contents | This paper studies the Manickam-Miklós-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 Erdős--Rényi 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Manickam-Miklós-Singhi Property in Graphs and Hypergraphs Džavoronok, Adam Combinatorics 05D05 This paper studies the Manickam-Miklós-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 Erdős--Rényi 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. |
| title | The Manickam-Miklós-Singhi Property in Graphs and Hypergraphs |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2605.22708 |