Polychromatic colorings of arbitrary rectangular partitions

A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex colorings using four colors of general partitions where every subrectangle is required to have all four colors appear on its boundary. It is shown that there exist general partitions that do not admit such a coloring. This answers a question of Dimitrov et al. [3]. It is also shown that the problem to determine if a given general partition has such a 4-coloring is NP-Complete. Some generalizations and related questions are also treated.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Dániel Gerbner, Balázs Keszegh, Nathan Lemons, Cory Palmer, Dömötör Pálvölgyi, Balázs Patkós
• Keywords: Arbitrary Number, DM 2010, General Partition, Non-overlapping Subrectangles