Intersection properties of boxes in \(R^ n\).

DOI10.1007/BF02579232zbMath0513.52009OpenAlexW2081078973MaRDI QIDQ1050625

Ludwig Danzer, Branko Grünbaum

Publication date: 1982

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02579232

zbMATH Keywords

convex setsconfigurationsboxesHelly-type theoremsn-pierceable

Mathematics Subject Classification ID

Other problems of combinatorial convexity (52A37) Helly-type theorems and geometric transversal theory (52A35) Designs and configurations (05B99)

Related Items (16)

Sets with convex closure which are unions of two starshaped sets and families of segments which have a 2-partition ⋮ Constrained square-center problems ⋮ Niche space, multigraphs, and the Helly condition ⋮ Intersection properties of boxes. I: An upper-bound theorem ⋮ j-partitions for visible shorelines ⋮ Helly-Type Theorems in Property Testing ⋮ A fractional Helly theorem for boxes ⋮ Discrete and lexicographic Helly-type theorems ⋮ On Wegner's inequality for axis-parallel rectangles ⋮ A note on the intersection property for flat boxes and boxicity in \(\mathbb R^d\) ⋮ 3-PIERCING OF d-DIMENSIONAL BOXES AND HOMOTHETIC TRIANGLES ⋮ About the piercing number of a family of intervals ⋮ 2-piercings via graph theory ⋮ On a conjecture of Danzer and Grünbaum ⋮ Fast stabbing of boxes in high dimensions ⋮ Staircase convex results for a certain class of orthogonal polytopes

Cites Work

• Common secants for families of polyhedra
• Polygons Circumscribed About Closed Convex Curves
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