English

Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II

Combinatorics 2012-10-30 v1

Abstract

Given positive integers k\geq 3 and r where k/2 \leq r \leq k-1, we give a minimum r-degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result. Our approach makes use of the absorbing method, and builds on work in 'Exact minimum degree thresholds for perfect matchings in uniform hypergraphs', where we proved the result for k divisible by 4.

Keywords

Cite

@article{arxiv.1210.7359,
  title  = {Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II},
  author = {Andrew Treglown and Yi Zhao},
  journal= {arXiv preprint arXiv:1210.7359},
  year   = {2012}
}

Comments

20 pages, 1 figure

R2 v1 2026-06-21T22:28:42.827Z