Every Large Point Set contains Many Collinear Points or an Empty Pentagon

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” conjecture of Kára, Pór, and Wood...

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Bibliographic Details
Published in:	Graphs and combinatorics Vol. 27; no. 1; pp. 47 - 60
Main Authors:	Abel, Zachary, Ballinger, Brad, Bose, Prosenjit, Collette, Sébastien, Dujmović, Vida, Hurtado, Ferran, Kominers, Scott Duke, Langerman, Stefan, Pór, Attila, Wood, David R.
Format:	Journal Article Publication
Language:	English
Published:	Japan Springer Japan 01.01.2011 Springer Nature B.V
Subjects:	05 Combinatorics 05D Extremal combinatorics 52 Convex and discrete geometry 52C Discrete geometry Classificació AMS Combinatorial analysis Combinatorics Convex geometry Discrete geometry Engineering Design Geometria Geometria convexa Geometria convexa i discreta Geometria discreta Geometry Graphs Hexagons Integers Matemàtiques i estadística Mathematics Mathematics and Statistics Original Paper Pentagon Planes Ramsey theory Ramsey, Teoria de Set theory Theorems Wood Àrees temàtiques de la UPC Happy end problem 05D10 (Ramsey theory) Erdős–Szekeres theorem 52C10 (Erdős problems and related topics of discrete geometry) Big line or big clique conjecture Empty quadrilateral Empty hexagon Empty pentagon
ISSN:	0911-0119, 1435-5914
Online Access:	Get full text
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