Skip to main content
SpringerLink
Log in

Legal coloring of graphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

The following computational problem was initiated by Manber and Tompa (22nd FOCS Conference, 1981): Given a graphG=(V, E) and a real functionf:V→R which is a proposed vertex coloring. Decide whetherf is a proper vertex coloring ofG. The elementary steps are taken to be linear comparisons.

Lower bounds on the complexity of this problem are derived using the chromatic polynomial ofG. It is shown how geometric parameters of a space partition associated withG influence the complexity of this problem.

Existing methods for analyzing such space partitions are suggested as a powerful tool for establishing lower bounds for a variety of computational problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. P. Dobkin andR. J. Lipton, On the complexity of computations under varying sets of primitives,J. Computer and System Science,18 (1979), 86–91.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. Greene, Acyclic orientations (Notes),in: Higher Combinatorics (M. Aigner, ed.), pp. D. Reidel, Dordrecht, 1977, 65–68.

  3. B. Grünbaum,Convex Polytopes, Interscience, New York, 1967.

    MATH  Google Scholar 

  4. R. L. Graham, A. C. Yao andF. F. Yao, Information bounds are weak in the shortest distance problem,J. Assoc. Comp. Mach.,27 (1980), 428–444.

    MATH  MathSciNet  Google Scholar 

  5. U. Manber andM. Tompa, The effect of number of Hamiltonian paths on the complexity of a vertex coloring problem.Proc. 22nd Annual Symposium on the Foundations of Computer Science, 1981.

  6. R. Rivest andA. C. Yao, On the polyhedral decision problem,SIAM J. Computing,9 (1980), 343–347.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Snir, Proving lower bounds for linear decision trees,in: Proc. 8th. International Coll. on Automata Languages and Programming, Lecture Notes in Computer Science 115, Springer Verlag, (1981), 305–315.

  8. R. P. Stanley, Acyclic orientations of graphs,Discrete Math.,5 (1973), 171–178.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. Zaslavsky,Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes, Mem. AMS. 154, Amer. Math. Soc., Providence, R. I., 1975.

    Google Scholar 

  10. T. Zaslavsky, The geometry of root systems and signed graphs,Amer. Math. Monthly (1981), 88–105.

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Hebrew University, 91 904, Jerusalem, Israel

    N. Linial

Authors
  1. N. Linial
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Linial, N. Legal coloring of graphs. Combinatorica 6, 49–54 (1986). https://doi.org/10.1007/BF02579408

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579408

AMS subject classification (1980)

Search

Navigation