Polygon Vertex Extremality and Decomposition of Polygons

Details Polygon Vertex Extremality and Decomposition of Polygons Polygon Vertex Extremality and Decomposition of Polygons

2010-04-11

arxiv.org/abs/1004.1852v1

Mathematics

Metric Geometry

10 pages, 6 figures

Scientific paper

In this paper, we show that if we decompose a polygon into two smaller polygons, then by comparing the number of extremal vertices in the original polygon versus the sum of the two smaller polygons, we can gain at most two globally extremal vertices in the smaller polygons, as well as at most two locally extremal vertices. We then will derive two discrete Four-Vertex Theorems from our results.

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