Transversal packings in families of percolated hypergraphs
Jie Han, Jie Hu, Shunan Wei, Donglei Yang

TL;DR
This paper proves that under certain minimum degree conditions, a random subhypergraph system almost surely contains a transversal $F$-factor, extending recent results and establishing near-optimal probability bounds.
Contribution
It extends existing results on transversal packings in hypergraphs by establishing probabilistic thresholds for the existence of $F$-factors in random subhypergraphs under minimum degree conditions.
Findings
High probability existence of transversal $F$-factors in random subhypergraphs.
Optimality of the probability threshold up to a constant factor.
A spread version of a known result on perfect matchings in $k$-partite hypergraphs.
Abstract
Let be a strictly -balanced -graph on vertices with edges and be the infimum of such that for every and sufficiently large , every -graph system on the same vertices with , contains a transversal -factor, that is, an -factor consisting of exactly one edge from each . In this paper we prove the following result. Let be a -graph system where each is an -vertex -graph with . Then with high probability contains a transversal -factor, where is a random subhypergraph of and…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · Stochastic processes and statistical mechanics
