%0 Journal Article
%T Three Colorability of an Arrangement Graph of Great Circles
%A I. Cahit
%J Mathematics
%D 2004
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0408363v1