Title of article :
Polychromatic colorings of arbitrary rectangular partitions
Author/Authors :
Gerbner، نويسنده , , Dلniel and Keszegh، نويسنده , , Balلzs and Lemons، نويسنده , , Nathan and Palmer، نويسنده , , Cory and Pلlvِlgyi، نويسنده , , Dِmِtِr and Patkَs، نويسنده , , Balلzs، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2010
Pages :
10
From page :
21
To page :
30
Abstract :
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.
Keywords :
Polychromatic colorings , Rectangular partitions
Journal title :
Discrete Mathematics
Serial Year :
2010
Journal title :
Discrete Mathematics
Record number :
1599205
Link To Document :
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