Immersed polygons and their diagonal triangulations
Alexander Ivanov, Alexey Avgustinovich Tuzhilin · Izvestiya Mathematics · 2008
We introduce the notion of an `immersed polygon', which naturally extends the notion of an ordinary planar polygon bounded by a closed (embedded) polygonal arc to the case when this arc may have self-intersections. We prove that every immersed polygon admits a diagonal triangulation and the closure of every embedded monotone polygonal arc bounds an immersed polygon. Given any non-degenerate planar linear tree, we construct an immersed polygon containing it.