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 …

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 …

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 …

Brualdi and Hollingsworth conjectured that, for even n, in a proper edge coloring of using
precisely colors, the edge set can be partitioned into spanning trees which are rainbow (and …

More than ten years ago in 2008, a new kind of graph coloring appeared in graph theory,
which is the {\it rainbow connection coloring} of graphs, and then followed by some other …

We seek the maximum number of colors in an edge‐coloring of the complete graph not
having t edge‐disjoint rainbow spanning subgraphs of specified types. Let,, and denote the …

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours.
The study of rainbow subgraphs goes back to the work of Euler on Latin squares. This article …

Given an undirected and edge-colored graph G, a rainbow component of G is a subgraph of
G having all the edges with different colors. The Rainbow Spanning Forest Problem consists …