The Upper‐Bound Theorem for Families of Boxes in ℝ d

DOI10.1112/S0025579300000176zbMath1175.52006MaRDI QIDQ3515262

Jürgen Eckhoff

Publication date: 29 July 2008

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

intersection graphclique numberaxis-aligned parallelotopes

Mathematics Subject Classification ID

Other problems of combinatorial convexity (52A37) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

• Intersection patterns of convex sets
• Face vectors of flag complexes
• Characterization of f-vectors of families of convex sets in \({\mathbb{R}}^ d\). I: Necessity of Eckhoff's conditions
• A simple proof of the upper bound theorem
• An upper-bound theorem for families of convex sets
• Characterization of f-vectors of families of convex sets in \({\mathbb{R}}^ d\). II: Sufficiency of Eckhoff's conditions
• Intersection properties of boxes. I: An upper-bound theorem
• Intersection properties of boxes. II: Extremal families
• Extremal interval graphs

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