English

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.

Keywords

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}
}

Comments

13 pages

R2 v1 2026-06-22T14:54:10.068Z