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 -