2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68190Alon et al. introduced the concept of non-repetitive colourings of graphs. Here we address some questions regarding non-repetitive colourings of planar graphs. Specifically, we show that the faces of any outerplanar map can be non-repetitively coloured using at most five colours. We also give some lower bounds for the number of colours required to non-repetitively colour the vertices of both outerplanar and planar graphs.4 pages, 2 figuresCombinatorics05C15text