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- Article
Every Large Point Set Contains Many Collinear Points or an Empty Pentagon
By: Zachary Abel, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott Duke Kominers, Stefan Langerman, Attila Pór and David Wood
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique”...
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Keywords:
Erdős-Szekeres Theorem;
Happy End Problem;
Big Line Or Big Clique Conjecture;
Empty Quadrilateral;
Empty Pentagon;
Empty Hexagon
Abel, Zachary, Brad Ballinger, Prosenjit Bose, Sébastien Collette, Vida Dujmović, Ferran Hurtado, Scott Duke Kominers, Stefan Langerman, Attila Pór, and David Wood. "Every Large Point Set Contains Many Collinear Points or an Empty Pentagon." Graphs and Combinatorics 27, no. 1 (January 2011): 47–60.
- 16 May 2012
- Research & Ideas
Can Decades of Military Overspending be Fixed?
37 states participate in the development and production program. The empty weight of the aircraft is 31,670 pounds and the wing area is 840 square feet. The aircraft has two engines generating 35,000 pounds of thrust, enabling the F-22 to...
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- Web
Podcast - Managing the Future of Work
empty nester or if a parent or other senior that’s been living with you goes into some type of care facility so you’re no longer that primary caregiver, your circumstances can change. But I think an overarching impression we had is that,...
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