TY - JOUR

T1 - Polychromatic colorings of rectangular partitions

AU - Dimitrov, Darko

AU - Horev, Elad

AU - Krakovski, Roi

PY - 2009/5/6

Y1 - 2009/5/6

N2 - 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.

AB - 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.

KW - Polychromatic colorings

KW - Rectangular partitions

UR - http://www.scopus.com/inward/record.url?scp=67349192163&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2008.07.035

DO - 10.1016/j.disc.2008.07.035

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AN - SCOPUS:67349192163

SN - 0012-365X

VL - 309

SP - 2957

EP - 2960

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

ER -