We solve a problem of Krivelevich, Kwan and Sudakov concerning the threshold for the
containment of all bounded degree spanning trees in the model of randomly perturbed …

A perfect H-tiling in a graph G is a collection of vertex-disjoint copies of a graph H in G that
together cover all the vertices in G. In this paper we investigate perfect H-tilings in a random …

A perfect K r‐tiling in a graph G is a collection of vertex‐disjoint copies of K r that together
cover all the vertices in G. In this paper we consider perfect K r‐tilings in the setting of …

For k≥ 2 and r≥ 1 such that k+ r≥ 4, we prove that, for any α> 0, there exists ε> 0 such that
the union of an n‐vertex k‐graph with minimum codegree and a binomial random k‐graph …

We study the existence of powers of Hamiltonian cycles in graphs with large minimum
degree to which some additional edges have been added in a random manner. It follows …

We prove that for integers $2\leq\ell< k $ and a small constant $ c $, if a $ k $-uniform
hypergraph with linear minimum codegree is randomlyperturbed'by changing non-edges to …

Given graphs H1, H2, a graph G is (H1, H2)-Ramsey if, for every colouring of the edges of G
with red and blue, there is a red copy of H1 or a blue copy of H2. In this paper we investigate …

A classical result of Komlós, Sárközy, and Szemerédi states that every n‐vertex graph with
minimum degree at least (1/2+ o (1)) n contains every n‐vertex tree with maximum degree …

For integers k≥ 3 and 1≤ ℓ≤ k− 1, we prove that for any α> 0, there exist ϵ> 0 and C> 0
such that for sufficiently large n∈(k− ℓ) N, the union of a k-uniform hypergraph with minimum …

We study Hamiltonicity in random subgraphs of the hypercube $\mathcal {Q}^ n $. Our first
main theorem is an optimal hitting time result. Consider the random process which includes …