Multiple Coverings with Closed Polygons

  • István Kovács
  • Géza Tóth
Keywords: Multiple Covering, Decomposition


A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are cover-decomposable. Here we show that closed, centrally symmetric convex polygons are also cover-decomposable. We also show that an infinite-fold covering of the plane with translates of $P$ can be decomposed into two infinite-fold coverings. Both results hold for coverings of any subset of the plane.

Author Biographies

István Kovács, Budapest University of Technology and Economics
Department of Computer Science and Informatics, student
Géza Tóth, Renyi Institute, Hungarian Academy of Sciences
research fellow
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