Rainbow Hamiltonicity in uniformly coloured perturbed digraphs Page 1 Combinatorics,
Probability and Computing (2024), 1–19 doi:10.1017/S0963548324000130 ARTICLE Rainbow …

The {\em discrepancy} of a matrix $ M\in\mathbb {R}^{d\times n} $ is given by $\mathrm
{DISC}(M):=\min_ {\boldsymbol {x}\in\{-1, 1\}^ n}\| M\boldsymbol {x}\| _\infty $. An outstanding …

Let G be a graph obtained as the union of some n-vertex graph H n with minimum degree δ
(H n)≥ α n and a d-dimensional random geometric graph G d (n, r). We investigate under …

Extremal properties of sparse graphs, randomly perturbed by the binomial random graph are
considered. It is known that every $ n $-vertex graph $ G $ contains a complete minor of …

Let $\tilde K_t $ denote the $3 $-uniform linear clique of order $ t $. Given an even integer $
t\geq 4$, let $ M $ denote the asymmetric maximal density of $\tilde K_t $ and $\tilde K_ {t/2} …

For a given $\delta\in (0, 1) $, the randomly perturbed graph model is defined as the union of
any $ n $-vertex graph $ G_0 $ with minimum degree $\delta n $ and the binomial random …

For any small constant $\epsilon> 0$, the Erd\H {o} sR\'enyi random graph $ G (n,\frac
{1+\epsilon}{n}) $ with high probability has a unique largest component which contains …

We consider the problem of finding a copy of a rainbow spanning bounded-degree tree in
the uniformly edge-coloured randomly perturbed graph. Let G0 be an n-vertex graph with …