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},
  pages={233-243}
}
A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following: 1. a monochromatic double star with at least 3n+1 4 vertices; 2. a monochromatic subgraph H such that all pairs of X ⊂ V (Kn) are at… CONTINUE READING
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