English

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

R2 v1 2026-06-21T15:09:07.974Z