Displaying similar documents to “Colouring polytopic partitions in ℝ d ”

Colouring polytopic partitions in ℝ d

Michal Křížek (2002)

Mathematica Bohemica

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We consider face-to-face partitions of bounded polytopes into convex polytopes in ℝ d for arbitrary d ≥ 1 and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed d + 1 . Partitions of polyhedra in ℝ 3 into pentahedra and hexahedra are 5 - and 6 -colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.

Finding H -partitions efficiently

Simone Dantas, Celina M. H. de Figueiredo, Sylvain Gravier, Sulamita Klein (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the concept of an H -partition of the vertex set of a graph G , which includes all vertex partitioning problems into four parts which we require to be nonempty with only external constraints according to the structure of a model graph H , with the exception of two cases, one that has already been classified as polynomial, and the other one remains unclassified. In the context of more general vertex-partition problems, the problems addressed in this paper have these properties:...