Carathéodory's theorem in depth
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Publication:2408186
DOI10.1007/s00454-017-9893-8zbMath1376.52012arXiv1509.04575OpenAlexW2963783010WikidataQ61732464 ScholiaQ61732464MaRDI QIDQ2408186
Ruy Fabila-Monroy, Clemens Huemer
Publication date: 10 October 2017
Published in: Lecture Notes in Computer Science, Discrete \& Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1509.04575
Erd?s problems and related topics of discrete geometry (52C10) Helly-type theorems and geometric transversal theory (52A35)
Related Items (2)
On weighted sums of numbers of convex polygons in point sets ⋮ Holes and islands in random point sets
Cites Work
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- A simpler proof of the Boros-Füredi-Bárány-Pach-Gromov theorem
- Computing optimal islands
- Witness (Delaunay) graphs
- Singularities, expanders and topology of maps. II: From combinatorics to topology via algebraic isoperimetry
- On Gromov's method of selecting heavily covered points
- Stabbing simplices by points and flats
- On a notion of data depth based on random simplices
- Points surrounding the origin
- The number of triangles covering the center of an \(n\)-set
- On empty triangles determined by points in the plane
- A generalization of Caratheodory's theorem
- Konvexe Fünfecke in ebenen Punktmengen
- A positive fraction Erdős-Szekeres theorem
- A Tverberg-type result on multicolored simplices
- Chromatic variants of the Erdős--Szekeres theorem on points in convex position.
- Colourful and fractional \((p,q)\)-theorems
- Covering the convex quadrilaterals of point sets
- Very colorful theorems
- The empty hexagon theorem
- Empty convex hexagons in planar point sets
- On the number of edges in geometric graphs without empty triangles
- Planar sets with few empty convex polygons
- A Further Generalization of the Colourful Carathéodory Theorem
- Helly’s theorem: New variations and applications
- Multidimensional Sorting
- Sets with No Empty Convex 7-Gons
- Empty Simplices in Euclidean Space
- A Problem of Geometry in R n
- Planar point sets with a small number of empty convex polygons
- On the Connectedness and Diameter of a Geometric Johnson Graph
- A Theorem on General Measure
- On An Invariant of Plane Regions and Mass Distributions
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