2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223222Given a set equipped with a transitive action of a group, we define the notion of an almost invariant coloring of the set. We consider the mapping class group orbit of a multicurve on a compact surface, and prove that in the case of genus at least two, no such almost invariant coloring exists. Conversely, in the case of a closed torus, one may find almost invariant colorings using arbitrarily many colors.15 pages, 4 figures, LaTeX; corrected one bibliography entryDifferential GeometryGeometric Topologytext