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Every Large Point Set contains Many Collinear Points or an Empty Pentagon
- Source :
- Graphs and Combinatorics 27(1), (2011), 47-60
- Publication Year :
- 2009
-
Abstract
- We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next open case of the "big line or big clique" conjecture of K\'ara, P\'or, and Wood [\emph{Discrete Comput. Geom.} 34(3):497--506, 2005].
- Subjects :
- Mathematics - Combinatorics
Computer Science - Computational Geometry
52C10, 05D10
Subjects
Details
- Database :
- arXiv
- Journal :
- Graphs and Combinatorics 27(1), (2011), 47-60
- Publication Type :
- Report
- Accession number :
- edsarx.0904.0262
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00373-010-0957-2