Colouring Polytopic Partitions in �
نویسنده
چکیده
We consider face-to-face partitions of bounded polytopes into convex polytopes in 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 3 into pentahedra and hexahedra are 5and 6-colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.
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