An Explicit Construction for a Ramsey Problem

@article{Mubayi2004AnEC,
  title={An Explicit Construction for a Ramsey Problem},
  author={Dhruv Mubayi},
  journal={Combinatorica},
  year={2004},
  volume={24},
  pages={313-324}
}
An explicit coloring of the edges of Kn is constructed such that every copy of K4 has at least four colors on its edges. As n → ∞, the number of colors used is n. This improves upon the previous bound of O(n) due to Erdős and Gyárfás obtained by probabilistic methods. The exponent 1/2 is optimal, since it is known that at least Ω(n) colors are required in such a coloring. The coloring is related to constructions giving lower bounds for the multicolor Ramsey number rk(C4). It is more complicated… CONTINUE READING