A unified approach to distance-two colouring of graphs on surfaces

@article{Amini2013AUA,
  title={A unified approach to distance-two colouring of graphs on surfaces},
  author={Omid Amini and Louis Esperet and Jan van den Heuvel},
  journal={Combinatorica},
  year={2013},
  volume={33},
  pages={253-296}
}
AbstractIn this paper we introduce the notion of Σ-colouring of a graph G: For given subsets Σ(v) of neighbours of v, for every v∈V (G), this is a proper colouring of the vertices of G such that, in addition, vertices that appear together in some Σ(v) receive different colours. This concept generalises the notion of colouring the square of graphs and of cyclic colouring of graphs embedded in a surface. We prove a general result for graphs embeddable in a fixed surface, which implies asymptotic… 
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