## Abstract

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 Goncalves 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 planar unavoidable. In addition, we prove that all trees of radius at most 2 are planar unavoidable and there are trees of radius 3 that are planar avoidable. We also address the planar unavoidable notion in more than two colors.

Original language | English |
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Article number | P4.9 |

Journal | Electronic Journal of Combinatorics |

Volume | 26 |

Issue number | 4 |

ISSN | 1097-1440 |

Publication status | Published - 1 Jan 2019 |