Covering by squares

L. Salinas, E. Goles

Research output: Contribution to journalArticlepeer-review


In this paper we introduce the "do not touch" condition for squares in the discrete plane. We say that two squares "do not touch" if they do not share any vertex or any segment of an edge. Using this condition we define a covering of the discrete plane, the covering can be strong or weak, regular or non-regular. For simplicity, in this article, we will restrict our attention to regular coverings, i.e., only a size is allowed for the squares and all the squares have the same number of adjacent squares. We establish minimal conditions for the existence of a weak or strong regular covering of the discrete plane, and we give a bound for the number of adjacent squares with respect to the size of the squares in the regular covering.

Original languageEnglish
Pages (from-to)10-27
Number of pages18
JournalTheoretical Computer Science
Issue number1-3
StatePublished - 10 May 2008
Externally publishedYes


  • Covering
  • Discrete geometry
  • Tiling


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