Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree
Journal of Combinatorial Theory Series B
Graph Theory
Perfect matchings in large uniform hypergraphs with large minimum collective degree
Journal of Combinatorial Theory Series A
The minimum degree threshold for perfect graph packings
Combinatorica
On Perfect Matchings in Uniform Hypergraphs with Large Minimum Vertex Degree
SIAM Journal on Discrete Mathematics
Combinatorics, Probability and Computing
Research paper: Combinatorial and computational aspects of graph packing and graph decomposition
Computer Science Review
On the co-degree threshold for the Fano plane
European Journal of Combinatorics
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Given hypergraphs H and F, an F-factor in H is a spanning subgraph consisting of vertex-disjoint copies of F. Let K"4^3-e denote the 3-uniform hypergraph on 4 vertices with 3 edges. We show that for any @c0 there exists an integer n"0 such that every 3-uniform hypergraph H of order nn"0 with minimum codegree at least (1/2+@c)n and 4|n contains a (K"4^3-e)-factor. Moreover, this bound is asymptotically the best possible and we further give a conjecture on the exact value of the threshold for the existence of a (K"4^3-e)-factor. Thereby, all minimum codegree thresholds for the existence of F-factors are known asymptotically for 3-uniform hypergraphs F on 4 vertices.