Monochromatic components in edge-colored complete uniform hypergraphs

@article{Kirly2011MonochromaticCI,
  title={Monochromatic components in edge-colored complete uniform hypergraphs},
  author={Zolt{\'a}n Kir{\'a}ly},
  journal={Electronic Notes in Discrete Mathematics},
  year={2011},
  volume={38},
  pages={517-521}
}
Let Kr n denote the complete r-uniform hypergraph on vertex set V = [n]. An f -coloring is a coloring of the edges with colors {1, 2, . . . , f}, it defines monochromatic r-uniform hypergraphs Hi = (V,Ei) for i = 1, . . . , f , where Ei contains the r-tuples colored by i. The connected components of hypergraphs Hi are called monochromatic components. For n > rk let f(n, r, k) denote the maximum number of colors, such that in any f -coloring of Kr n, there exist k monochromatic components… CONTINUE READING

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