Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints

@article{Alon2003ProperlyCS,
  title={Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints},
  author={Noga Alon and Tao Jiang and Zevi Miller and Dan Pritikin},
  journal={Random Struct. Algorithms},
  year={2003},
  volume={23},
  pages={409-433}
}
We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m,G) denote the smallest n such that every m-good edge-coloring of Kn yields a properly edgecolored copy of G, and let g(m,G) denote the smallest n such that every m-good edge-coloring of Kn yields a rainbow copy of G. We give bounds on f(m,G) and g(m,G). For complete graphs G = Kt, we have c1mt/ ln t ≤ f… CONTINUE READING