We solve the existence problem for $ F $-designs for arbitrary $ r $-uniform hypergraphs $ F
$. This implies that given any $ r $-uniform hypergraph $ F $, the trivially necessary …

We prove the existence of block designs in complexes and hypergraphs whose clique
distribution satisfies appropriate regularity constraints. As a special case, this gives a new …

High-girth Steiner triple systems Page 1 Annals of Mathematics 200 (2024), 1059–1156
https://doi.org/10.4007/annals.2024.200.3.4 High-girth Steiner triple systems By Matthew Kwan …

A fundamental theorem of Wilson states that, for every graph F, every sufficiently large F-
divisible clique has an F-decomposition. Here a graph G is F-divisible if e (F) divides e (G) …

For all integers n≥ k> d≥ 1, let md (k, n) be the minimum integer D≥ 0 such that every k-
uniform n-vertex hypergraph H with minimum d-degree δ d (H) at least D has an optimal …

We prove several results about substructures in Latin squares. First, we explain how to
adapt our recent work on high-girth Steiner triple systems to the setting of Latin squares …

We study the F-decomposition threshold δ F for a given graph F. Here an F-decomposition of
a graph G is a collection of edge-disjoint copies of F in G which together cover every edge of …

Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …

The iterative absorption method has recently led to major progress in the area of (hyper‐)
graph decompositions. Among other results, a new proof of the existence conjecture for …

Our main result is that every graph G on n≥ 10 4 r 3 vertices with minimum degree δ
(G)≥(1− 1/10 4 r 3/2) n has a fractional K r-decomposition. Combining this result with recent …