Name
Abstract | ||
|---|---|---|
Given two k-graphs (k-uniform hypergraphs) F and H, a perfect F-tiling (or F-factor) in H is a set of vertex-disjoint copies of F that together cover the vertex set of H. For all complete k-partite k-graphs K, Mycroft proved a minimum codegree condition that guarantees a K-factor in an n-vertex k-graph, which is tight up to an error term o(n). In this paper we improve the error term in Mycroft's result to a sublinear term that relates to the Turan number of K when the differences of the sizes of the vertex classes of K are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling K-(k)(1, . . . , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1017/S096354831900021X | COMBINATORICS PROBABILITY & COMPUTING |
DocType | Volume | Issue |
Journal | 28 | 6 |
ISSN | Citations | PageRank |
0963-5483 | 0 | 0.34 |
References | Authors | |
0 | 3 | |