A graph labeling is an assignment of integers to the vertices or edges, or both, subject to
certain conditions. Graph labelings were first introduced in the mid 1960s. In the intervening …

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 …

An edge-coloured graph is said to be rainbow if no colour appears more than once.
Extremal problems involving rainbow objects have been a focus of much research over the …

The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K2n+ 1 into
edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n …

A celebrated theorem of Pippenger states that any almost regular hypergraph with small
codegrees has an almost perfect matching. We show that one can find such an almost …

Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …

In 2001, Komlós, Sárközy and Szemerédi proved that, for each α> 0, there is some c> 0 and
n 0 such that, if n≥ n 0, then every n-vertex graph with minimum degree at least (1/2+ α) n …

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 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 …

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 …