Ramsey‐type results for Gallai colorings

@article{Gyrfs2010RamseytypeRF,
  title={Ramsey‐type results for Gallai colorings},
  author={Andr{\'a}s Gy{\'a}rf{\'a}s and G{\'a}bor N. S{\'a}rk{\"o}zy and Andr{\'a}s Seb{\"o} and Stanley M. Selkow},
  journal={Journal of Graph Theory},
  year={2010},
  volume={64}
}
A Gallai‐coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Gallai‐colorings occur in various contexts such as the theory of partially ordered sets (in Gallai's original paper) or information theory. Gallai‐colorings extend 2‐colorings of the edges of complete graphs. They actually turn out to be close to 2‐colorings—without being trivial extensions. Here, we give a method to extend some results on 2‐colorings to Gallai‐colorings, among… 
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References

SHOWING 1-10 OF 46 REFERENCES
Size of Monochromatic Double Stars in Edge Colorings
TLDR
It is shown that in every r-coloring of the edges of Kn there is a monochromatic double star with at least n(r+1)+r-1}{r^2+1} vertices, which improves a bound of Mubayi for the largest monochromeatic subgraph of diameter at most three.
Edge colorings of complete graphs without tricolored triangles
We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the
Finding Large p-Colored Diameter Two Subgraphs
TLDR
It is shown for k≥1 and k\2≤p≤k that there is always a p-colored diameter two subgraph of Kn containing at least vertices and that this is best possible up to an additive constant l satisfying 0≤l.
Domination in colored complete graphs
TLDR
There exists X c V(K,) such that 1x1 I t and X monochromatically dominates all but at most n/2’ vertices of K, and X can be constructed by a fast greedy algorithm.
Edge-colored complete graphs with precisely colored subgraphs
TLDR
The main object of this paper is to describe the behavior of the functionf(s,t;k), usually thinking ofs andt fixed, and lettingk become large.
Lambda composition
TLDR
The decomposition of a graph into its lambda subgraphs is described and this is used to prove the decomposition theorem of Gallai.
Recent results on generalized Ramsey theory for graphs
Virtually all of the known results on generalized Ramsey theory for graphs have been reported here, and the most general method of proof was brute force. There is certainly a need for more powerful
Generalizing the Ramsey Problem through Diameter
TLDR
The results include determining $f_1^k(K_n)$, which is equivalent to determining classical Ramsey numbers for multicolorings, and a construction due to Calkin implies that $f-3^k (K-n) \le {{n}\over {k-1}} + k-1$ when $k- 1$ is a prime power.
A note on perfect graphs
Let the lines of a complete graph be 3-colored so that no triangle gets 3 different colors. If two of these colors form perfect graphs then so does the third.
...
1
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