Covering a square by small perimeter rectangles

N. Alon, D. J. Kleitman

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m2).

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalDiscrete & Computational Geometry
Issue number1
StatePublished - Dec 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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