Given a collection $\mathcal {G}=(G_1,\dots, G_h) $ of graphs on the same vertex set $ V $
of size $ n $, an $ h $-edge graph $ H $ on the vertex set $ V $ is a $\mathcal {G} …

A subgraph of an edge‐coloured graph is called rainbow if all its edges have distinct
colours. The study of rainbow subgraphs goes back more than 200 years to the work of …

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours.
Our main result implies that, given any optimal colouring of a sufficiently large complete …

The Lovasz Local Lemma is a seminal result in probabilistic combinatorics. It gives a
sufficient condition on a probability space and a collection of events for the existence of an …

In 1989, Rota made the following conjecture. Given bases in an-dimensional vector space,
one can always find disjoint bases of, each containing exactly one element from each (we …

We study approximate decompositions of edge‐colored quasirandom graphs into rainbow
spanning structures: an edge‐coloring of a graph is locally‐bounded if every vertex is …

A subgraph of an edge-coloured complete graph is called rainbow if all its edges have
different colours. The study of rainbow decompositions has a long history, going back to the …

We prove a rainbow version of the blow‐up lemma of Komlós, Sárközy, and Szemerédi for
μn‐bounded edge colorings. This enables the systematic study of rainbow embeddings of …

We prove two results regarding cycles in properly edge-colored graphs. First, we make a
small improvement to the recent breakthrough work of Alon, Pokrovskiy and Sudakov who …

The Lovász local lemma is a seminal result in probabilistic combinatorics. It gives a sufficient
condition on a probability space and a collection of events for the existence of an outcome …