A Note on Exact Minimum Degree Threshold for Fractional Perfect Matchings

@article{Lu2022ANO,
  title={A Note on Exact Minimum Degree Threshold for Fractional Perfect Matchings},
  author={Hongliang Lu and Xingxing Yu},
  journal={Graphs and Combinatorics},
  year={2022},
  volume={38},
  pages={1-8}
}
Rödl, Ruciński, and Szemerédi determined the minimum $$(k-1)$$ ( k - 1 ) -degree threshold for the existence of fractional perfect matchings in k -uniform hypergrahs, and Kühn, Osthus, and Townsend extended this result by asymptotically determining the d -degree threshold for the range $$k-1>d\ge k/2$$ k - 1 > d ≥ k / 2 . In this note, we prove the following exact degree threshold: let k ,  d be positive integers with $$k\ge 4$$ k ≥ 4 and $$k-1>d\ge k/2$$ k - 1 > d ≥ k / 2 , and let n be any… 

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