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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Michael D Plummer; Bjarne Toft; VANDERBILT UNIV NASHVILLE TN. |

OCLC Number: | 227691606 |

Description: | 14 p. |

### Abstract:

This paper, all graphs will be finite, loopless and will have no parallel lines. Let G be a 2-connected planar graph with <V(G)>=p 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.

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