Rainbow Generalizations of Ramsey Theory: A Survey Page 1 Graphs and Combinatorics (2010)
26:1–30 DOI 10.1007/s00373-010-0891-3 SURVEY Rainbow Generalizations of Ramsey …

In 1959, Erdős and Gallai proved the asymptotically optimal bound for the maximum number
of edges in graphs not containing a path of a fixed length. Here, we study a rainbow version …

Abstract Let G:=(G 1, G 2, G 3) be a triple of graphs on the same vertex set V of size n. A
rainbow triangle in G is a triple of edges (e 1, e 2, e 3) with ei∈ G i for each i and {e 1, e 2, e …

We study a Tur\'an-type problem on edge-colored complete graphs. We show that for any $ r
$ and $ t $, any sufficiently large $ r $-edge-colored complete graph on $ n $ vertices with …

One of the most fundamental results in graph theory is Mantel's theorem which determines
the maximum number of edges in a triangle-free graph of order $ n $. Recently a colorful …

Abstract Let G≔(G 1, G 2, G 3) G:=(G_1,G_2,G_3) be a triple of graphs on a common vertex
set VV of size n n. A rainbow triangle in GG is a triple of edges (e 1, e 2, e 3) (e_1,e_2,e_3) …

We study the extremal properties of coloured multigraphs H, whose edge set is the union of
two simple graphs H r and H b (thought of as red and blue edges) on the same vertex set …

We study Turán‐and Ramsey‐type problems on edge‐colored graphs. A two‐edge‐colored
graph is called ε ε‐balanced if each color class contains at least an ε ε‐proportion of its …

We say that $ k $ graphs $ G_1, G_2,\dots, G_k $ on a common vertex set of size $ n $
contain a rainbow copy of a graph $ H $ if their union contains a copy of $ H $ with each …

Classical questions in extremal graph theory concern the asymptotics of ex (G, H) where H is
a fixed family of graphs and G= G n is taken from a “standard” increasing sequence of host …