Let G and H be hypergraphs on n vertices, and suppose H has large enough minimum
degree to necessarily contain a copy of G as a subgraph. We give a general method to …

For a graph GG and p∈ 0, 1 p ∈\left 0, 1\right, we denote by G p G _p the random
sparsification of GG obtained by keeping each edge of GG independently, with probability p …

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 …

Consider any dense r-regular quasirandom bipartite graph H with parts of size n and fix a set
of r colours. Let L be a random list assignment where each colour is available for each edge …

We give a simple method to estimate the number of distinct copies of some classes of
spanning subgraphs in hypergraphs with a high minimum degree. In particular, for each, by …

We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our
main result states that the minimum d-degree threshold for loose Hamiltonicity relative to the …

We study conditions under which a given hypergraph is randomly robust Hamiltonian, which
means that a random sparsification of the host graph contains a Hamilton cycle with high …

A family of $ r $ distinct sets $\{A_1,\ldots, A_r\} $ is an $ r $-sunflower if for all $1\leqslant i<
j\leqslant r $ and $1\leqslant i'< j'\leqslant r $, we have $ A_i\cap A_j= A_ {i'}\cap A_ {j'} …

A randomly perturbed graph $ G^ p= G_\alpha\cup G (n, p) $ is obtained by taking a
deterministic $ n $-vertex graph $ G_\alpha=(V, E) $ with minimum degree $\delta …

A seminal result of Koml\'os, S\'ark\" ozy, and Szemer\'edi states that any n-vertex graph G
with minimum degree at least (1/2+{\alpha}) n contains every n-vertex tree T of bounded …