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 …

Given a graph H, the k‐colored Gallai‐Ramsey number grk (K 3⁢: H) is defined to be the
minimum integer n such that every k‐coloring (using all k colors) of the complete graph on n …

We prove that every 3-coloring of the edges of the complete graph on n vertices without a
rainbow triangle contains a set of order Ω (n 1/3 log 2⁡ n) which uses at most two colors …

The original work on Gallai-Ramsey numbers from this perspective [1] was initiated in
meetings between Ralph Faudree, Ron Gould, Mike Jacobson, and Colton Magnant, on a …

An edge coloring of a graph G is a Gallai coloring if it contains no rainbow triangle. We show
that the number of Gallai r-colorings of K_n is (r2+o(1))2^n2. This result indicates that almost …

Given a graph G, we consider the problem of finding the minimum number n such that any k
edge colored complete graph on n vertices contains either a three colored triangle or a …

Given a graph HH, the kk‐colored Gallai–Ramsey number grk (K 3: H) gr_k(K_3:H) is
defined to be the minimum integer nn such that every kk‐coloring of the edges of the …

Motivated by Ramsey-type questions, we consider edge-colorings of complete graphs and
complete bipartite graphs without rainbow path. Given two graphs G and H, the k-colored …

For graphs G and H and integer k ≥ 1 k≥ 1, the Gallai–Ramsey number gr_k (G: H) grk (G:
H) is defined to be the minimum integer N such that if K_N KN is edge-colored with k colors …

Consider the graph consisting of a triangle with a pendant edge. We describe the structure
of rainbow‐free edge colorings of a complete graph and provide some corresponding Gallai …