Properly coloured copies and rainbow copies of large graphs with small maximum degree

@article{Bttcher2012ProperlyCC,
  title={Properly coloured copies and rainbow copies of large graphs with small maximum degree},
  author={Julia B{\"o}ttcher and Yoshiharu Kohayakawa and Aldo Procacci},
  journal={Random Struct. Algorithms},
  year={2012},
  volume={40},
  pages={425-436}
}
Let G be a graph on n vertices with maximum degree ∆. We use the Lovász local lemma to show the following two results about colourings χ of the edges of the complete graph Kn. If for each vertex v of Kn the colouring χ assigns each colour to at most (n − 2)/(22.4∆2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by χ. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409–433, 2003]. On the other hand, if… CONTINUE READING

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