Abstract
Given a set P of m⩾3 points in general position in the plane, we want to find the smallest possible number of convex polygons with vertices in P such that the edges of all these polygons contain all the m2 straight line segments determined by the points of P. We show that if m is odd, the answer is (m2-1)/8 regardless of the choice of P. In this case there is even a partitioning of the edges of the complete geometric graph on m vertices into (m2-1)/8 convex polygons. The answer in the case where m is even depends on the choice of P and not only on m. Nearly tight lower and upper bounds follow in the case where m is even.
Original language | English |
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Pages (from-to) | 957-974 |
Number of pages | 18 |
Journal | Discrete and Computational Geometry |
Volume | 72 |
Issue number | 2 |
DOIs | |
State | Published - Sep 2024 |
Keywords
- 52C99
- Concave chains
- Convex chains
- Convex polygons
- Geometric graphs
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics