Illuminating and covering convex bodies

DOI10.1016/j.disc.2014.08.013zbMath1303.52009arXiv1308.0791OpenAlexW2075808811MaRDI QIDQ465282

Christian Richter, Horst Martini, Margarita Spirova

Publication date: 31 October 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0791

zbMATH Keywords

covering numbersHadwiger's covering problemcentral illuminationillumination numbersparallel illuminationtranslative coverings

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15)

Related Items (7)

Covering the boundary of a convex body with its smaller homothetic copies ⋮ Borsuk's problem, Boltyanski's illumination problem, and circumradius ⋮ Estimations of covering functionals of simplices ⋮ Starshaped sets ⋮ On parallel packing and covering of squares and cubes ⋮ On covering functionals of convex bodies ⋮ Online unit covering in Euclidean space

Cites Work

• On translative coverings of convex bodies
• Illumination and exposition of a convex \(n\)-dimensional body depending on its sharpness
• Symmetrization of closure operators and visibility
• Classical topics in discrete geometry
• Combinatorial problems on the illumination of convex bodies
• On Grünbaum's conjecture about inner illumination of convex bodies
• Illumination and visibility problems in terms of closure operators
• Invariant illumination of convex bodies
• On the vertex index of convex bodies
• The illumination conjecture and its extensions
• On the successive illumination parameters of convex bodies
• Excursions into combinatorial geometry
• External analysis of boundary points of convex sets: illumination and visibility
• Quantitative Illumination of Convex Bodies and Vertex Degrees of Geometric Steiner Minimal Trees
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