Authors
Darko Dimitrov, Elad Horev, Roi Krakovski
Publication date
2009/5/6
Journal
Discrete mathematics
Volume
309
Issue
9
Pages
2957-2960
Publisher
North-Holland
Description
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.
Total citations
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Scholar articles
D Dimitrov, E Horev, R Krakovski - Discrete mathematics, 2009