2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140647Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small isotopy. We also show how to obtain sharper constants when the starting curve is smooth. We apply our main theorem to prove a limiting result for essential subarcs of a knot.12 pages, 3 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 2008Geometric Topology57M25 (Primary); 05C10, 57M15 (Secondary)text