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<p>In this paper, we determine the minimum degree threshold of perfect matchings with high discrepancy in <i>r</i>-edge-colored <i>k</i>-uniform hypergraphs for all <i>k</i> ⩾ 3 and <i>r</i> ⩾ 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 et al. (2024) concerning 3-uniform hypergraphs.</p>

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Discrepancies of perfect matchings in hypergraphs

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • Hongliang Lu,
  • Jie Ma,
  • Shengjie Xie

摘要

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 ⩾ 3 and r ⩾ 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 et al. (2024) concerning 3-uniform hypergraphs.