Polychromatic colorings of rectangular partitions

Darko Dimitrov, Elad Horev, Roi Krakovski

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


A rectangular partition is a partition of a plane rectangle into an arbitrary number of non-overlapping rectangles such that no four rectangles share a corner. In this note, it is proven that every rectangular partition admits a vertex coloring with four colors such that every rectangle, except possibly the outer rectangle, has all four colors on its boundary. This settles a conjecture of Dinitz et al. [Y. Dinitz, M.J. Katz, R. Krakovski, Guarding rectangular partitions, in: Abstracts 23rd Euro. Workshop Comput. Geom., 2007, pp. 30-33]. The proof is short, simple and based on 4-edge-colorability of a specific class of planar graphs.

Original languageEnglish
Pages (from-to)2957-2960
Number of pages4
JournalDiscrete Mathematics
Issue number9
StatePublished - 6 May 2009
Externally publishedYes


  • Polychromatic colorings
  • Rectangular partitions


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