We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.

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Persistent URL dx.doi.org/10.1007/s00373-017-1816-1
Journal Graphs and Combinatorics
Bose, P, Dujmović, V, Morin, P. (Pat), & Rioux-Maldague, L. (Lucas). (2017). New Bounds for Facial Nonrepetitive Colouring. Graphs and Combinatorics, 33(4), 817–832. doi:10.1007/s00373-017-1816-1