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 …

Consider a host hypergraph $ G $ which contains a spanning structure due to minimum
degree considerations. We collect three results proving that if the edges of $ G $ are …

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 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 …

At the middle of the last century, discrete mathematics and combinatorics established
themselves as foundational areas of mathematics with numerous applications, especially in …

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 …

The celebrated canonical Ramsey theorem of Erd\H {o} s and Rado implies that for $2\leq
k\in\mathbb {N} $, any colouring of the edges of $ K_n $ with $ n $ sufficiently large gives a …