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Polychromatic Colorings of n-Dimensional Guillotine-Partitions

  • Balázs Keszegh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

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.

Keywords

Plane Graph Left Face Bipartite Plane Graph Rooted Binary Tree 24th European Workshop 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Balázs Keszegh
    • 1
  1. 1.Central European UniversityBudapest 

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