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- W1528987669 abstract "A strong hyperbox-respecting coloring of an n-dimensional hyperbox partition is a coloring of the corners of its hyperboxes with 2 n colors such that any hyperbox has all the colors appearing on its corners. A guillotine-partition is obtained by starting with a single axis-parallel hyperbox and recursively cutting a hyperbox of the partition into two hyperboxes by a hyperplane orthogonal to one of the n axes. We prove that there is a strong hyperbox-respecting coloring of any n-dimensional guillotine-partition. This theorem generalizes the result of Horev et al. [8] who proved the 2-dimensional case. This problem is a special case of the n-dimensional variant of polychromatic colorings. The proof gives an efficient coloring algorithm as well." @default.
- W1528987669 created "2016-06-24" @default.
- W1528987669 creator A5077727901 @default.
- W1528987669 date "2008-08-12" @default.
- W1528987669 modified "2023-09-23" @default.
- W1528987669 title "Polychromatic Colorings of n-Dimensional Guillotine-Partitions" @default.
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- W1528987669 doi "https://doi.org/10.1007/978-3-540-69733-6_12" @default.
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