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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 planardoi:10.5445/ir/1000099292 fatcat:hyyrhtsuuza25bidox3ybuip7q