Cyclic Coloration of 3-Polytopes,

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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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA175241

Entities

People

  • Bjarne Toft
  • Michael D. Plummer

Organizations

  • Vanderbilt University

Tags

DTIC Thesaurus Topics

  • Analogs
  • Boundaries
  • Contracts
  • Graph Theory
  • Inequalities
  • Mathematics
  • Notation
  • Tennessee
  • Triangles
  • Universities

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.