TY - JOUR
T1 - Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II
AU - Treglown, A.
AU - Zhao, Y.
PY - 2013/9/1
Y1 - 2013/9/1
N2 - Given positive integers k ≥ 3 and ℓ where k/2 ≤ ℓ ≤ k - 1, we give a minimum ℓ-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, and extends work of Rödl, Ruciński and Szemerédi who determined the threshold for ℓ = k - 1. Our approach makes use of the absorbing method, and builds on earlier work, where we proved the result for k divisible by 4.
AB - Given positive integers k ≥ 3 and ℓ where k/2 ≤ ℓ ≤ k - 1, we give a minimum ℓ-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, and extends work of Rödl, Ruciński and Szemerédi who determined the threshold for ℓ = k - 1. Our approach makes use of the absorbing method, and builds on earlier work, where we proved the result for k divisible by 4.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84877359564&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2013.04.008
DO - 10.1016/j.jcta.2013.04.008
M3 - Article
AN - SCOPUS:84877359564
SN - 0097-3165
VL - 120
SP - 1463
EP - 1482
JO - Journal of Combinatorial Theory, Series A
JF - Journal of Combinatorial Theory, Series A
IS - 7
ER -