A Problem of Geometry in R n

No abstract is available for this paper.

• Publication year

  1979

• Venue

  Unknown venue

• Publication date

  1979-07-01

• Fields of study

  Mathematics

• Identifiers
  DOI 10.2307/2042758
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Combinatorial Geometry in the Plane

  1964cited by this paper
• On components in some families of sets

  1961cited by this paper

• Helly-type problems from a topological perspective

  2026cites this paper
• On Lines Crossing Pairwise Intersecting Convex Sets in Three Dimensions

  2026influential citation
• Intersection patterns of set systems on manifolds with slowly growing homological shatter functions

  2026cites this paper
• Quantitative Helly-type problems

  2025cites this paper
• Helly-type theorems for separated $d$-intervals

  2025cites this paper
• Colorful Helly via induced matchings

  2025cites this paper
• Helly-type theorems for monotone properties of boxes

  2025cites this paper
• New Sufficient Conditions for Linear-Sized Epsilon-Nets and $(p,2)$-Theorems

  2025influential citation
• Piercing intersecting convex sets

  2024cites this paper
• A note on infinite versions of $(p,q)$-theorems

  2024cites this paper
• The fractional Helly number for separable convexity spaces

  2024cites this paper
• Towards the methodology for solving the minimum enclosing ball and related problems

  2024cites this paper
• No-Dimensional Helly’s Theorem in Uniformly Convex Banach Spaces

  2024cites this paper
• Helly type problems in convexity spaces

  2024cites this paper
• Beyond Chromatic Threshold via (p, q)-Theorem, and Blow-Up Phenomenon

  2024influential citation
• The Helly number of Hamming balls and related problems

  2024cites this paper
• Beyond chromatic threshold via the $(p,q)$-theorem, and a sharp blow-up phenomenon

  2024cites this paper
• The Quantitative Fractional Helly theorem

  2024cites this paper
• Quantitative Helly-type Theorems via Hypergraph Chains

  2023cites this paper
• Colorful Helly Theorem for Piercing Boxes with Two Points

  2022cites this paper
• Colorful two-piercing theorem for boxes

  2022cites this paper
• Intersection patterns in spaces with a forbidden homological minor

  2021cites this paper
• Helly-type problems

  2021cites this paper
• Pairwise intersecting convex sets and cylinders in $\R^3$

  2021cites this paper
• Fractional Helly Theorem for Cartesian Products of Convex Sets

  2021cites this paper
• Workshop ( hybrid meeting ) : Discrete Geometry Table of Contents

  2021cites this paper
• Mathematisches Forschungsinstitut Oberwolfach Report No . 30 / 2020 DOI : 10 . 4171 / OWR / 2020 / 30 Discrete Geometry Organized

  2020cites this paper
• Quantitative Fractional Helly and $(p,q)$-Theorems

  2020cites this paper
• Optimal Bounds for the Colorful Fractional Helly Theorem

  2020cites this paper
• Large Cliques in Hypergraphs with Forbidden Substructures

  2020cites this paper
• Large Cliques in Hypergraphs with Forbidden Substructures

  2019cites this paper
• Intersection Patterns of Planar Sets

  2019cites this paper
• Radon numbers grow linearly

  2019cites this paper
• Radon Numbers Grow Linearly

  2019cites this paper
• Further Consequences of the Colorful Helly Hypothesis

  2018cites this paper
• Improved bounds on the Hadwiger–Debrunner numbers

  2018cites this paper
• Theorems of Carathéodory, Helly, and Tverberg Without Dimension

  2018influential citation
• The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg

  2017cites this paper
• Nerves, minors, and piercing numbers

  2017cites this paper
• A Note on Testing Intersection of Convex Sets in Sublinear Time

  2016cites this paper
• Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets

  2016cites this paper
• Quantitative Combinatorial Geometry for Continuous Parameters

  2016cites this paper
• A note on extremal results on directed acyclic graphs

  2016cites this paper
• HELLY-TYPE THEOREMS AND GEOMETRIC TRANSVERSALS

  2016cites this paper
• A note on the colorful fractional Helly theorem

  2015influential citation
• Carathéodory’s Theorem in Depth

  2015cites this paper
• HELLY NUMBERS OF SUBSETS OF $ \ MATHBB R ^ D $ AND SAMPLING TECHNIQUES IN OPTIMIZATION By

  2015cites this paper
• A Note on Smaller Fractional Helly Numbers

  2015cites this paper
• Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of $S$-optimization

  2015cites this paper
• Positive-fraction intersection results and variations of weak epsilon-nets

  2015cites this paper
• Helly‐type theorems for the diameter

  2015cites this paper
• Helly's Theorem: New Variations and Applications

  2015cites this paper
• Helly numbers of subsets of ℝᵈ and sampling techniques in optimization

  2015cites this paper
• Fractional Turan's theorem and bounds for the chromatic number

  2015cites this paper
• Extremal results on intersection graphs of boxes in $R^d$

  2014cites this paper
• A Variant of the Hadwiger–Debrunner (p, q)-Problem in the Plane

  2014cites this paper
• A fractional Helly theorem for boxes

  2014influential citation
• Helly-Type Theorems in Property Testing

  2013cites this paper
• Colourful and Fractional (p,q)-theorems

  2013cites this paper
• Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey

  2011cites this paper
• On Order Types of Systems of Segments in the Plane

  2010cites this paper
• NEW RESULTS FOR T ( k )-FAMILIES IN THE PLANE

  2010cites this paper
• A Note on Geometric 3-Hypergraphs

  2010cites this paper
• Transversal numbers over subsets of linear spaces

  2010cites this paper
• Transversal Numbers over Subsets of Linear Spaces and Helly Type Certificates of Mixed Integer Infeasibility

  2009influential citation
• d-collapsibility is NP-complete for d>=4

  2009cites this paper
• Dimension Gaps between Representability and Collapsibility

  2009cites this paper
• Топологические методы в комбинаторной геометрии@@@Topological methods in combinatorial geometry

  2008cites this paper
• On the Complexity of Recognition of 2-collapsibility

  2008cites this paper
• On the gap between representability and collapsibility

  2008cites this paper
• On the Complexity of Recognition of 2-collapsibility

  2008cites this paper
• d-collapsibility is NP-complete for d greater or equal to 4

  2008cites this paper
• Applications of Graph and Hypergraph Theory in Geometry

  2007cites this paper
• k-Sets and k-Facets

  2007cites this paper
• Berge's theorem, fractional Helly, and art galleries

  2006cites this paper
• On a topological fractional Helly theorem

  2005cites this paper
• No Helly Theorem for Stabbing Translates by Lines in R3

  2004cites this paper
• Bounded VC-Dimension Implies a Fractional Helly Theorem

  2004cites this paper
• A fractional Helly theorem for convex lattice sets

  2003cites this paper
• Transversal numbers for hypergraphs arising in geometry

  2002cites this paper
• Transversal Numbers for Hypergraphs Arising inGeometryNoga

  2001cites this paper
• Piercing and Selection Theorems in Convexity (lecture Notes)

  1999cites this paper
• A Tverberg-type result on multicolored simplices

  1996cites this paper
• A purely combinatorial proof of the Hadwiger Debrunner (p, q) Conjecture

  1996cites this paper
• Bounding the piercing number

  1995influential citation
• Piercing convex sets

  1992cites this paper
• Piercing convex sets and the hadwiger-debrunner (p

  1992influential citation
• Intersection properties of boxes. Part I: An upper-bound theorem

  1988influential citation
• Geometric permutations and common transversals

  1986cites this paper
• Intersection patterns of convex sets

  1984influential citation
• Intersection Patterns of Families of Convex Sets

  1982cites this paper