Three Colorability of an Arrangement Graph of Great Circles
Combinatorics
2007-05-23 v1
Abstract
Stan Wagon asked the following in 2000. Is every zonohedron face 3-colorable when viewed as a planar map? An equivalent question, under a different guise, is the following: is the arrangement graph of great circles on the sphere always vertex 3-colorable? (The arrangement graph has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points.) Assume that no three circles meet at a point, so that this arrangement graph is 4-regular. In this note we have shown that all arrangement graphs defined as above are 3-colorable.
Cite
@article{arxiv.math/0408363,
title = {Three Colorability of an Arrangement Graph of Great Circles},
author = {I. Cahit},
journal= {arXiv preprint arXiv:math/0408363},
year = {2007}
}
Comments
6 pages, 4 figures