Colouring of graphs with Ramsey-type forbidden subgraphs

@article{Dabrowski2014ColouringOG,
  title={Colouring of graphs with Ramsey-type forbidden subgraphs},
  author={Konrad Dabrowski and Petr A. Golovach and Dani{\"e}l Paulusma},
  journal={Theor. Comput. Sci.},
  year={2014},
  volume={522},
  pages={34-43}
}
A colouring of a graph G = (V,E) is a mapping c : V → {1, 2, . . .} such that c(u) 6= c(v) if uv ∈ E; if |c(V )| ≤ k then c is a k-colouring. The Colouring problem is that of testing whether a given graph has a k-colouring for some given integer k. If a graph contains no induced subgraph isomorphic to any graph in some family H, then it is called H-free. The complexity of Colouring for H-free graphs with |H| = 1 has been completely classified. When |H| = 2, the classification is still wide open… CONTINUE READING
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