Piercing convex sets and the Hadwiger-Debrunner \((p,q)\)-problem
From MaRDI portal
Publication:1206503
DOI10.1016/0001-8708(92)90052-MzbMath0768.52001OpenAlexW2009545408MaRDI QIDQ1206503
Publication date: 1 April 1993
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0001-8708(92)90052-m
Related Items
On piercing numbers of families satisfying the \((p,q)_{r}\) property, The \((p, q)\)-extremal problem and the fractional chromatic number of Kneser hypergraphs, Improved bounds on weak \(\varepsilon\)-nets for convex sets, Bounding the piercing number, Note on a problem of M. Talagrand, A note on the colorful fractional Helly theorem, Helly-type theorems for the diameter, Improved bounds on the Hadwiger-Debrunner numbers, A family of convex sets in the plane satisfying the (4, 3)-property can be pierced by nine points, On optimal piercing of a square, Helly-gap of a graph and vertex eccentricities, The geometry and combinatorics of discrete line segment hypergraphs, Hitting simplices with points in \(\mathbb R^{3}\), Guarding galleries where every point sees a large area, Quantitative Tverberg theorems over lattices and other discrete sets, Radon numbers grow linearly, A counterexample to a conjecture of Grünbaum on piercing convex sets in the plane, Combinatorial properties of nonarchimedean convex sets, From a \((p, 2)\)-theorem to a tight \((p, q)\)-theorem, Further consequences of the colorful Helly hypothesis, Topological drawings meet classical theorems from convex geometry, Bounds on piercing and line-piercing numbers in families of convex sets in the plane, Fractional Helly theorem for Cartesian products of convex sets, Theorems of Carathéodory, Helly, and Tverberg without dimension, Piercing numbers for balanced and unbalanced families, Foundations of a theory of convexity on affine Grassmann manifolds, A definable \((p,q)\)-theorem for NIP theories, Using Brouwer’s Fixed Point Theorem, An optimal generalization of the colorful Carathéodory theorem, Piercing translates and homothets of a convex body, Berge's theorem, fractional Helly, and art galleries, Helly’s theorem: New variations and applications, Nerves, minors, and piercing numbers, On transversals of quasialgebraic families of sets, On weak \(\epsilon\)-nets and the Radon number, The \((p, q)\) property in families of \(d\)-intervals and \(d\)-trees, On transversal numbers of intersecting straight line systems and intersecting segment systems, Quantitative fractional Helly and \((p,q)\)-theorems, On transversal and 2-packing numbers in uniform linear systems, Colourful linear programming, Quantitative combinatorial geometry for continuous parameters, Colourful and fractional \((p,q)\)-theorems, Weak \(\varepsilon \)-nets have basis of size \(O(1/\varepsilon\log (1/\varepsilon))\) in any dimension, Lower bounds for weak epsilon-nets and stair-convexity, On Wegner's inequality for axis-parallel rectangles, Quantitative \((p, q)\) theorems in combinatorial geometry, Reprint of: Weak \(\varepsilon\)-nets have basis of size \(O(1/{\epsilon}\log (1/\epsilon))\) in any dimension, On a problem of Danzer, Piercing all translates of a set of axis-parallel rectangles, Radon numbers and the fractional Helly theorem, Unnamed Item, From a $(p,2)$-Theorem to a Tight $(p,q)$-Theorem, Unnamed Item, Tverberg’s theorem is 50 years old: A survey, Stabbing pairwise intersecting disks by five points, Quantitative combinatorial geometry for concave functions, VC-dimension and Erdős-Pósa property, About the piercing number of a family of intervals, A variant of the Hadwiger-Debrunner \((p,q)\)-problem in the plane, A note on smaller fractional Helly numbers, A new lower bound on Hadwiger-Debrunner numbers in the plane, On a Problem of Danzer, The (2,2) and (4,3) Properties in Families of Fat Sets in the Plane, The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg, Dimension gaps between representability and collapsibility, Externally definable sets and dependent pairs II, Further Consequences of the Colorful Helly Hypothesis, Piercing numbers in approval voting, Some Themes Around First Order Theories Without the Independence Property, Topological Drawings Meet Classical Theorems from Convex Geometry, On a problem by Dol'nikov, Helly-type problems, About an Erdős-Grünbaum conjecture concerning piercing of non-bounded convex sets, Transversal numbers for hypergraphs arising in geometry, Piercing all translates of a set of axis-parallel rectangles, A fractional Helly theorem for convex lattice sets
Cites Work
- Intersection patterns of convex sets
- Über eine Variante zum Hellyschen Satz
- A simple proof of the upper bound theorem
- An upper-bound theorem for families of convex sets
- The number of triangles covering the center of an \(n\)-set
- A generalization of Caratheodory's theorem
- d-collapsing and nerves of families of convex sets
- Über eine kombinatorisch-geometrische Frage von Hadwiger und Debrunner
- Intersectional properties of certain families of compact convex sets
- A Problem of Geometry in R n
- A Generalization of Radon's Theorem
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item