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Indecomposable Coverings

  • János Pach (a1), Gábor Tardos (a2) and Géza Tóth (a3)
Abstract

We prove that for every k > 1, there exist k-fold coverings of the plane (i) with strips, (ii) with axis-parallel rectangles, and (iii) with homothets of any fixed concave quadrilateral, that cannot be decomposed into two coverings. We also construct for every k > 1 a set of points P and a family of disks in the plane, each containing at least k elements of P, such that, no matter how we color the points of P with two colors, there exists a disk D all of whose points are of the same color.

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References
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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