Year: 2024
Type: article
Abstract: Introducing the notions of distant pairs of vertices and big subtriangles of a polygon, and using extremal graph theory—specifically, Tutan's graph—we establish upper bounds for: the sum of distances between all distant pairs of vertices in polygons with unit perimeter, and the sum of areas of all big subtriangles in convex polygons with unit area. We also formulate a conjecture on the upper bound of the sum of the areas of all subtriangles in a convex polygon.
Author: Gonchigdorzh Radnaasumberel
Institution: Mongolian National University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4414190817
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