Ordered Ramsey numbers

@article{Conlon2017OrderedRN,
  title={Ordered Ramsey numbers},
  author={David Conlon and Jacob Fox and Choongbum Lee and Benny Sudakov},
  journal={J. Comb. Theory, Ser. B},
  year={2017},
  volume={122},
  pages={353-383}
}
Abstract Given a labeled graph H with vertex set { 1 , 2 , … , n } , the ordered Ramsey number r ( H ) is the minimum N such that every two-coloring of the edges of the complete graph on { 1 , 2 , … , N } contains a copy of H with vertices appearing in the same order as in H . The ordered Ramsey number of a labeled graph H is at least the Ramsey number r ( H ) and the two coincide for complete graphs. However, we prove that even for matchings there are labelings where the ordered Ramsey number… Expand
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