# Planar Ramsey graphs

@article{Axenovich2019PlanarRG,
title={Planar Ramsey graphs},
author={Maria Axenovich and Carsten Thomassen and Ursula Schade and Torsten Ueckerdt},
journal={Electron. J. Comb.},
year={2019},
volume={26},
pages={4}
}
• Published 3 December 2018
• Mathematics
• Electron. J. Comb.
We say that a graph $H$ is planar unavoidable if there is a planar graph $G$ such that any red/blue coloring of the edges of $G$ contains a monochromatic copy of $H$, otherwise we say that $H$ is planar avoidable. That is, $H$ is planar unavoidable if there is a Ramsey graph for $H$ that is planar. It follows from the Four-Color Theorem and a result of Gonçalves that if a graph is planar unavoidable then it is bipartite and outerplanar. We prove that the cycle on $4$ vertices and any path are…

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