Higher-Dimensional Analogues of the Map Coloring Problem

  title={Higher-Dimensional Analogues of the Map Coloring Problem},
  author={Bhaskar Bagchi and Basudeb Datta},
  journal={The American Mathematical Monthly},
  pages={733 - 737}
  • B. Bagchi, B. Datta
  • Published 1 February 2012
  • Mathematics
  • The American Mathematical Monthly
Abstract After a brief discussion of the history of the problem, we propose a generalization of the map coloring problem to higher dimensions. 

Ball packings with high chromatic numbers from strongly regular graphs



The Problem of the Thirteen Spheres

  • J. Leech
  • Philosophy, Mathematics
    The Mathematical Gazette
  • 1956
An independent proof of this impossibility of David Gregory's conjecture that a sphere can touch thirteen non-overlapping spheres equal to it is outlined.

Geometry and Topology of 3-manifolds

Low-dimensional topology is an extremely rich eld of study, with many dierent and interesting aspects. The aim of this project was to expand upon work previously done by I. R. Aitchison and J.H.

The Journey of the Four Colour Theorem Through Time

The Four Colour Theorem is one of the simplest mathematical problems to state and understand. It says that any planar map is four-colourable. In other words, given a map, one can colour its regions

Sphere packings, I

  • T. Hales
  • Physics, Mathematics
    Discret. Comput. Geom.
  • 1997
A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.

Every Planar Map Is Four Colorable

As has become standard, the four color map problem will be considered in the dual sense as the problem of whether the vertices of every planar graph (without loops) can be colored with at most four

The problem of the thirteen spheres

A famous controversy between David Gregory and Isaac Newton in 1694 concerned the following question: How many unit spheres can simultaneously touch a given sphere of the same size?


This paper is concerned with the investigation of properties of convex polyhedra in Lobacevskiĭ spaces; it gives a complete description of convex bounded polyhedra with dihedral angles not exceeding

The kissing number in four dimensions

The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three