Abstract:
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.
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