Three Colorability of an Arrangement Graph of Great Circles

Details Three Colorability of an Arrangement Graph of Great Circles Three Colorability of an Arrangement Graph of Great Circles

2004-08-26

arxiv.org/abs/math/0408363v1

Mathematics

Combinatorics

6 pages, 4 figures

Scientific paper

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.

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