Polygon Vertex Extremality and Decomposition of Polygons
Metric Geometry
2010-04-13 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1004.1852,
title = {Polygon Vertex Extremality and Decomposition of Polygons},
author = {Wiktor J. Mogilski},
journal= {arXiv preprint arXiv:1004.1852},
year = {2010}
}
Comments
10 pages, 6 figures