Cyclic Coloration of 3-Polytopes,
VANDERBILT UNIV NASHVILLE TN
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This paper, all graphs will be finite, loopless and will have no parallel lines. Let G be a 2-connected planar graph with VGp points. Suppose G has some fixed imbedding Phi G approaches R-sq in the plane. The pair G Phi is often called a plane graph. A cyclic coloration of G Phi is an assignment to colors to the points of G such that for any face-bounding cycle F of G Phi, the points of F have different colors. The cyclic coloration number chi sub c G Phi is the minimum number of colors in any cyclic coloration of G, Phi. The main result of the present paper is to show that if G, Phi is a 3-connected plane graph, then chi sub c G, Phi p G, Phi 9. Moreover, if rho is sufficiently large of sufficiently large or sufficiently small, then this bound on chi sub c can be improved somewhat.
- Theoretical Mathematics