ORTHOGONAL COLORINGS OF THE SPHERE

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 184
  • Download : 0
An orthogonal coloring of the two-dimensional unit sphere S-2, is a partition of S-2 into parts such that no part contains a pair of orthogonal points: that is, a pair of points at spherical distance pi/2 apart. It is a well-known result that an orthogonal coloring of S-2 requires at least four parts, and orthogonal colorings with exactly four parts can easily be constructed from a regular octahedron centered at the origin. An intriguing question is whether or not every orthogonal 4-coloring of S-2 is such an octahedral coloring. In this paper, we address this question and show that if every color class has a non-empty interior, then the coloring is octahedral. Some related results are also given.
Publisher
LONDON MATH SOC
Issue Date
2016
Language
English
Article Type
Article
Keywords

CHROMATIC NUMBER; DISTANCE GRAPHS; CHOICE; AXIOM; PLANE

Citation

MATHEMATIKA, v.62, no.2, pp.492 - 501

ISSN
0025-5793
DOI
10.1112/S0025579315000303
URI
http://hdl.handle.net/10203/209571
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0