A New Bound for Hadwiger’s Covering Problem in \(\boldsymbol{\mathbb{E}}^3\)

DOI10.1137/22M1490314OpenAlexW4317035214MaRDI QIDQ5883269

Andriy Prymak

Publication date: 30 March 2023

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

Full work available at URL: https://doi.org/10.1137/22m1490314

zbMATH Keywords

linear programmingconvex bodycovering numberillumination numberillumination problemcovering by smaller homothetic copies

Mathematics Subject Classification ID

Linear programming (90C05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Other problems of combinatorial convexity (52A37) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (1)

On the multiple illumination numbers of convex bodies

Uses Software

• GitHub

Cites Work

• A quantitative program for Hadwiger's covering conjecture
• Überdeckung eines Eibereiches durch Parallelverschiebung seines offenen Kerns
• The difference body of a convex body
• Covering a three-dimensional convex body by smaller homothetic copies
• An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
• The geometry of homothetic covering and illumination
• Improved bounds for Hadwiger's covering problem via thin-shell estimates
• On the Hadwiger covering problem in low dimensions
• A note on coverings
• Covering the Boundary of a Convex Set by Tiles
• Spherical coverings and X-raying convex bodies of constant width

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