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 …

We study the model G α∪ G (n, p) of randomly perturbed dense graphs, where G α is any n‐
vertex graph with minimum degree at least α n and G (n, p) is the binomial random graph …

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 …

Given integers $ n\ge\Delta\ge 2$, let $\mathcal {T}(n,\Delta) $ be the collection of all $ n $-
vertex trees with maximum degree at most $\Delta $. A question of Alon, Krivelevich and …

Random graphs have played an integral role in extremal combinatorics since they were first
used by Erdos [30] to prove an exponential lower bound for Ramsey numbers. The binomial …

For positive integers d< k and n divisible by k, let md (k, n) be the minimum d-degree
ensuring the existence of a perfect matching in a k-uniform hypergraph. In the graph case …

Given D and γ> 0, whenever c> 0 is sufficiently small and n sufficiently large, if G is a family
of D-degenerate graphs of individual orders at most n, maximum degrees at most cn log⁡ n …

A subgraph of an edge-coloured graph is called rainbow if all its edges have different
colours. We prove a rainbow version of the blow-up lemma of Komlós, Sárközy, and …

The bandwidth theorem [Mathematische Annalen, 343 (1): 175--205, 2009] states that any $
n $-vertex graph $ G $ with minimum degree $\big (\tfrac {k-1}{k}+ o (1)\big) n $ contains all …

In recent years there has been much progress in graph theory on questions of the following
type. What is the threshold for a certain large substructure to appear in a random graph …