Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II
نویسندگان
چکیده
منابع مشابه
Exact minimum degree thresholds for perfect matchings in uniform hypergraphs
Article history: Received 19 August 2011 Available online xxxx Given positive integers k and where 4 divides k and k/2 k−1, we give a minimum -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, as well as the hypergrap...
متن کاملExact minimum degree thresholds for perfect matchings in uniform hypergraphs II
Given positive integers k ≥ 3 and l where k/2 ≤ l ≤ k − 1, we give a minimum ldegree 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 meth...
متن کاملExact Minimum Degree Thresholds for Perfect Matchings in Uniform Hypergraphs Iii
We determine the exact minimum l-degree threshold for perfect matchings in k-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 1 2 ( n k−l ) . This extends our previous results [18, 19] that determine the minimum l-degree thresholds for perfect matchings in k-uniform hypergraphs for all l ≥ k/2 and provides two new (exact) threshold...
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Given positive integers k and ` where k/2 ≤ ` ≤ k− 1, we give a minimum `-degree condition that ensures a perfect matching in a kuniform hypergraph. This condition is best possible and improves on work of Pikhurko [12] who gave an asymptotically exact result, and extends work of Rödl, Ruciński and Szemerédi [15] who determined the threshold for ` = k−1. Our approach makes use of the absorbing m...
متن کاملPerfect matchings in uniform hypergraphs with large minimum degree
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a perfect matching in terms of a variant of the minimum degree. We prove that for every k ≥ 3 and sufficiently large n, a perfect matching exists in every n-vertex k-uniform hypergraph in which each set of k − 1 vertices ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2013
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2013.04.008