Independence numbers of locally sparse graphs and a Ramsey type problem

@article{Alon1996IndependenceNO,
  title={Independence numbers of locally sparse graphs and a Ramsey type problem},
  author={N. Alon},
  journal={Random Struct. Algorithms},
  year={1996},
  volume={9},
  pages={271-278}
}
  • N. Alon
  • Published 1996
  • Computer Science
  • Random Struct. Algorithms
Let G = (V,E) be a graph on n vertices with average degree t ≥ 1 in which for every vertex v ∈ V the induced subgraph on the set of all neighbors of v is r-colorable. We show that the independence number of G is at least c log (r+1) n t log t, for some absolute positive constant c. This strengthens a well known result of Ajtai, Komlós and Szemerédi. Combining their result with some probabilistic arguments, we prove the following Ramsey type theorem, conjectured by Erdös in 1979. There exists an… Expand
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