Covering the plane with convex polygons

DOI10.1007/BF02187684zbMath0595.52015OpenAlexW1986134212MaRDI QIDQ1077728

János Pach

Publication date: 1986

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/130982

zbMATH Keywords

multiple coverings\(k\)-fold coveringcentrosymmetric convex closed polygondecomposition of coveringssimple coverings

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Polytopes and polyhedra (52B99) Combinatorial aspects of tessellation and tiling problems (05B45) Combinatorial aspects of packing and covering (05B40)

Related Items (21)

Convex polygons are cover-decomposable ⋮ Unsplittable coverings in the plane ⋮ Coloring Axis-Parallel Rectangles ⋮ Indecomposable coverings with concave polygons ⋮ Decomposition of multiple coverings into more parts ⋮ Set it and forget it: approximating the set once strip cover problem ⋮ Polychromatic colorings of unions of geometric hypergraphs ⋮ Coloring points with respect to squares ⋮ Colouring bottomless rectangles and arborescences ⋮ Changing of the guards: strip cover with duty cycling ⋮ Octants are cover-decomposable ⋮ Optimally decomposing coverings with translates of a convex polygon ⋮ Octants are cover-decomposable into many coverings ⋮ Colorful strips ⋮ Almost tight bounds for \(\epsilon\)-nets ⋮ Decomposition of multiple coverings into many parts ⋮ Multiple coverings with closed polygons ⋮ Coloring axis-parallel rectangles ⋮ Delaunay graphs of point sets in the plane with respect to axis‐parallel rectangles ⋮ Proper coloring of geometric hypergraphs ⋮ Indecomposable coverings with homothetic polygons

Cites Work

• The classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes
• Balanced two-colorings of finite sets in the square. I
• A note on Euclidean near neighbor searching in the plane
• Irregularities of distribution, VII
• On irregularities of distribution
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