# Accession Number:

## ADA175241

# Title:

## Cyclic Coloration of 3-Polytopes,

# Descriptive Note:

# Corporate Author:

## VANDERBILT UNIV NASHVILLE TN

# Personal Author(s):

# Report Date:

## 1985-01-01

# Pagination or Media Count:

## 14.0

# Abstract:

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.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics