Polychromatic colorings of arbitrary rectangular partitions

详细信息    查看全文

• 作者：Dá ; niel Gerbner ; Balá ; zs Keszegh ; Nathan Lemons ; Cory Palmer ; Dö ; mö ; tö ; r Pá ; lvö ; lgyi ; Balá ; zs Patkó ; s
• 关键词：Polychromatic colorings ; Rectangular partitions
• 刊名：Discrete Mathematics
• 出版年：2010
• 出版时间：6 January 2010
• 年：2010
• 卷：310
• 期：1
• 页码：21-30
• 全文大小：576 K

文摘

A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex 4-colorings 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. [D. Dimitrov, E. Horev, R. Krakovski, Polychromatic colorings of rectangular partitions, Discrete Mathematics 309 (2009) 2957–2960]. 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.