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Article

Grunbaum coloring and its generalization to arbitrary dimension

Australasian Journal of Combinatorics. 2017. Vol. 67. No. 2. P. 119-130.
M.N.Vyalyi, Lawrencenko S., Zgonnik L.

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 Grunbaum colorings, their existence and usage. In particular, one of the most striking significances of Grunbaum’s Conjecture in the 2-dimensional case is its equivalence to the 4-Color Theorem. The notion of Grunbaum coloring is extended from the 2-dimensional case to the case of arbitrary finite hyper-dimensions.