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arXiv · 2408.06020

Discrepancies of perfect matchings in hypergraphs

Hongliang Lu·Jie Ma·Shengjie Xie
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Abstract

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 Z\'arate-Guer\'en concerning 3-uniform hypergraphs.

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Hongliang Lu, Jie Ma, Shengjie Xie. 2024-08-12. Discrepancies of perfect matchings in hypergraphs. https://arxiv.org/abs/2408.06020

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