Ramsey Numbers of Ordered Graphs

  title={Ramsey Numbers of Ordered Graphs},
  author={Martin Balko and Josef Cibulka and Karel Kr'al and Jan Kyn{\vc}l},
  journal={Electronic Journal of Combinatorics},
An ordered graph is a pair $\mathcal{G}=(G,\prec)$ where $G$ is a graph and $\prec$ is a total ordering of its vertices. The ordered Ramsey number $\overline{R}(\mathcal{G})$ is the minimum number $N$ such that every ordered complete graph with $N$ vertices and with edges colored by two colors contains a monochromatic copy of $\mathcal{G}$. In contrast with the case of unordered graphs, we show that there are arbitrarily large ordered matchings $\mathcal{M}_n$ on $n$ vertices for which… Expand
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