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 …

We show that for any fixed dense graph G and bounded-degree tree T on the same number
of vertices, a modest random perturbation of G will typically contain a copy of T. This …

We show that for any n divisible by 3, almost all order‐n Steiner triple systems have a perfect
matching (also known as a parallel class or resolution class). In fact, we prove a general …

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 …

The blow-up lemma states that a system of super-regular pairs contains all bounded degree
spanning graphs as subgraphs that embed into a corresponding system of complete pairs …

Almost all Steiner triple systems are almost resolvable Page 1 Forum of Mathematics, Sigma
(2020), Vol. 8:e39, 1–24 doi:10.1017/fms.2020.29 RESEARCH ARTICLE Almost all Steiner triple …

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 …

We show that for every there exists C> 0 such that if then asymptotically almost surely the
random graph contains the kth power of a Hamilton cycle. This determines the threshold for …

A seminal result of Hajnal and Szemerédi states that if a graph G with n vertices has
minimum degree δ(G)≥(r-1)n/r for some integer r≥2, then G contains a K_r-factor …