Skip to main content
Log in

On-line coloring of perfect graphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

Lovász, Saks, and Trotter showed that there exists an on-line algorithm which will color any on-linek-colorable graph onn vertices withO(nlog(2k−3) n/log(2k−4) n) colors. Vishwanathan showed that at least Ω(logk−1 n/k k) colors are needed. While these remain the best known bounds, they give a distressingly weak approximation of the number of colors required. In this article we study the case of perfect graphs. We prove that there exists an on-line algorithm which will color any on-linek-colorable perfect graph onn vertices withn 10k/loglogn colors and that Vishwanathan's techniques can be slightly modified to show that his lower bound also holds for perfect graphs. This suggests that Vishwanathan's lower bound is far from tight in the general case.

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

Access this article

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. Bean: Effective coloration,J. Symbolic Logic 41 (1976), 469–480.

    Google Scholar 

  2. A. Gyárfás, andJ. Lehel: On-line and first-fit coloring of graphs,J. of Graph Theory 12 (1988), 217–227.

    Google Scholar 

  3. A. Gyárfás, andJ. Lehel: First-Fit and on-line chromatic number of families of graphs,Ars Combinatorica 29C (1990), 168–176.

    Google Scholar 

  4. S. Irani: Coloring inductive graphs on-line,Proceedings of the 3lst Annual Symposium on the Foundations of Computer Science, (1990), 470–479.

  5. H. A. Kierstead: The linearity of First-Fit for coloring interval graphs,SIAM J. on Discrete Math.,1 (1988), 526–530.

    Google Scholar 

  6. H. A. Kierstead, S. G. Penrice, andW. T. Trotter: First-Fit and on-line coloring of graphs which do not induceP 5,SIAM J. on Discrete Mathematics,8 (1995), 485–498.

    Google Scholar 

  7. H. A. Kierstead, S. G. Penrice, andW.T. Trotter: On-line graph coloring and recursive graph theory,SIAM J. on Discrete Math. 7 (1994), 72–89.

    Google Scholar 

  8. H. A. Kierstead, andW. T. Trotter: An extremal problem in recursive combinatorics,Congressus Numerantium,33 (1981), 143–153.

    Google Scholar 

  9. L. Lovász, M. Saks, andW. T. Trotter: An online graph coloring algorithm with sublinear performance ratio,Discrete Math., (1989), 319–325.

  10. M. Szegedy: Private communication.

  11. S. Vishwanathan: Randomized online graph coloring,J. Algorithms,13 (1992), 657–669.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by Office of Naval Research grant N00014-90-J-1206.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kierstead, H.A., Kolossa, K. On-line coloring of perfect graphs. Combinatorica 16, 479–491 (1996). https://doi.org/10.1007/BF01271267

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01271267

Mathematics Subject Classification (1991)

Navigation