Discrepancies of perfect matchings in hypergraphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913493144305664 |
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| author | Lu, Hongliang Ma, Jie Xie, Shengjie |
| author_facet | Lu, Hongliang Ma, Jie Xie, Shengjie |
| contents | In this paper, we determine the minimum degree threshold of perfect matchings with high discrepancy in $r$-edge-colored $k$-uniform hypergraphs for all $k\geq 3$ and $r\geq 2$, thereby completing the investigation into discrepancies of perfect matchings that has recently attracted significant attention. Our approach identifies this discrepancy threshold with a novel family of multicolored uniform hypergraphs and reveals new phenomena not covered in previous studies. In particular, our results address a question of Balogh, Treglown and Zárate-Guerén concerning 3-uniform hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06020 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrepancies of perfect matchings in hypergraphs Lu, Hongliang Ma, Jie Xie, Shengjie Combinatorics In this paper, we determine the minimum degree threshold of perfect matchings with high discrepancy in $r$-edge-colored $k$-uniform hypergraphs for all $k\geq 3$ and $r\geq 2$, thereby completing the investigation into discrepancies of perfect matchings that has recently attracted significant attention. Our approach identifies this discrepancy threshold with a novel family of multicolored uniform hypergraphs and reveals new phenomena not covered in previous studies. In particular, our results address a question of Balogh, Treglown and Zárate-Guerén concerning 3-uniform hypergraphs. |
| title | Discrepancies of perfect matchings in hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.06020 |