Proving the “expectation-threshold” conjecture of Kahn and Kalai [Combin. Probab. Comput.
16 (2007), pp. 495–502], we show that for any increasing property $\mathcal {F} $ on a finite …

Proving a conjecture of Talagrand, a fractional version of the``expectation-threshold"
conjecture of Kalai and the second author, we show that p_c(F)=O(q_f(F)log\ell(F)) for any …

A typical decomposition question asks whether the edges of some graph G can be
partitioned into disjoint copies of another graph H. One of the oldest and best known …

A Latin square of order $ n $ is an $ n $ by $ n $ grid filled using $ n $ symbols so that each
symbol appears exactly once in each row and column. A transversal in a Latin square is a …

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 Latin square is an $ n $ by $ n $ grid filled with $ n $ symbols so that each symbol appears
exactly once in each row and each column. A transversal in a Latin square is a collection of …

The hypercontractive inequality on the discrete cube plays a crucial role in many
fundamental results in the Analysis of Boolean functions, such as the KKL theorem …

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 …

Given a collection of graphs $\mathbf {G}=(G_1,\ldots, G_m) $ with the same vertex set, an $
m $-edge graph $ H\subset\cup_ {i\in [m]} G_i $ is a transversal if there is a bijection $\phi: E …

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 …