Graphs and Combinatorics

, Volume 6, Issue 2, pp 95–110 | Cite as

On a generalized family of colorings

  • Pierre Baldi
Original Papers

Abstract

Motivated by a question in cellular telecommunication technology, we investigate a family of graph coloring problems where several colors can be assigned to each vertex and no two colors are the same within any ball of radiusR. We find bounds and coloring algorithms for different kinds of graphs including trees,n-cycles, hypercubes and lattices. We briefly examine connections to Heawood's map color theorem and state a few conjectures and open problems.

Keywords

Generalize Family Open Problem Graph Coloring Coloring Problem Telecommunication Technology 
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References

  1. 1.
    Baldi, P.: (1) On a Generalized Family of Colorings (2) Some Contributions to the Theory of Neural Networks (3) Embeddings of Ultrametric Spaces. Ph.D. Thesis, California Institute of Technology, May 1986Google Scholar
  2. 2.
    Baldi, P., Posner, E.C.: Graph Coloring Bounds for Cellular Radio. International Journal of Computers and Mathematics with Applications.19, no. 10, 91–97 (1990)Google Scholar
  3. 3.
    Hoffman, A.J., Singleton, R.R.: On Moore Graphs with Diameter 2 and 3.IBM Journal Nov. 1960Google Scholar
  4. 4.
    Posner, E.C.: Frequency Assignment in Cellular Radio. In: Open Problems in Communication and Computation (T.M. Cover, B. Gopinath eds.) pp. 100–101. New York: Springer-Verlag 1987Google Scholar
  5. 5.
    Young, W.R.: Advanced Mobile Phone Service, Introduction Background and Objectives. Bell System Technical Journal59, 1–14 (1973)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Pierre Baldi
    • 1
  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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