Gr\"unbaum coloring and its generalization to arbitrary dimension
Combinatorics
2017-01-10 v1 Computational Complexity
Geometric Topology
History and Overview
Abstract
This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Gr\"unbaum colorings, their existence and usage. In particular, one of the most striking significances of Gr\"unbaum's Conjecture in the 2-dimensional case is its equivalence to the 4-Color Theorem. The notion of Gr\"unbaum coloring is extended from the 2-dimensional case to the case of arbitrary finite hyper-dimensions.
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Cite
@article{arxiv.1607.03959,
title = {Gr\"unbaum coloring and its generalization to arbitrary dimension},
author = {S. Lawrencenko and M. N. Vyalyi and L. V. Zgonnik},
journal= {arXiv preprint arXiv:1607.03959},
year = {2017}
}
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13 pages