Grünbaum coloring and its generalization to arbitrary dimension

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