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Coloring graphs on-line

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Online Algorithms

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References

  1. D. Bean. Effective coloration. J. Symbolic Logic, 41:469–480, 1976.

    Google Scholar 

  2. A. Blum and D. Karger. An O(n 3/14)-coloring for 3-colorable graphs. Preprint.

    Google Scholar 

  3. M. Chrobak and M. Ślusarek. On some packing problems relating to Dynamical Storage Allocations. RAIRO Informatique Theoretique, 22:487–499, 1988.

    Google Scholar 

  4. P. ErdŐs and A. Hajnal. On chromatic numbers of graphs and set systems. Acta Math. Sci. Hung., 17:61–99, 1966.

    Article  Google Scholar 

  5. S. Felsner. On-line chain partitions of orders. To appear in Theoret. Comput. Sci.

    Google Scholar 

  6. F. Galvin, I. Rival, and B. Sands. A Ramsey-type theorem for traceable graphs. J. Comb. Theory, Series B, 33:7–16, 1982.

    Google Scholar 

  7. A. Gyárfás. On Ramsey covering numbers. In Coll. Math. Soc. János Bolyai 10, Infinite and Finite Sets, pages 801–816. North-Holland/American Elsevier, New York, 1975.

    Google Scholar 

  8. A. Gyárfás. Problems from the world surrounding perfect graphs. Zastowania Matematyki Applicationes Mathemacticae, 19:413–441, 1985.

    Google Scholar 

  9. A. Gyárfás and J. Lehel. On-line and first-fit colorings of graphs. Journal of Graph Theory, 12:217–227, 1988.

    Google Scholar 

  10. A. Gyárfás and J. Lehel. Effective on-line coloring of P 5-free graphs. Combinatorica, 11:181–184, 1991.

    Article  Google Scholar 

  11. A. Gyárfás, E. Szemerédi, and Z. Tuza. Induced subtrees in graphs of large chromatic number. Discrete Math, 30:235–244, 1980.

    Google Scholar 

  12. S. Irani. Coloring inductive graphs on-line. Algorithmica, 11:53–72, 1994. Also in Proc. 31st IEEE Symposium on Foundations of Computer Science, 1990, 470–479.

    Article  Google Scholar 

  13. H. A. Kierstead. On-line coloring k-colorable graphs. To appear in Israel J. of Math.

    Google Scholar 

  14. H. A. Kierstead. An effective version of Dilworth's theorem. Trans. Amer. Math. Soc., 268:63–77, 1981.

    Google Scholar 

  15. H. A. Kierstead. Recursive colorings of highly recursive graphs. Canadian J. Math., 33:1279–1290, 1981.

    Google Scholar 

  16. H. A. Kierstead. An effective version of Hall's theorem. Proc. Amer. Math. Soc., 88:124–128, 1983.

    Google Scholar 

  17. H. A. Kierstead. The linearity of first-fit coloring of interval graphs. SIAM Journal on Discrete Math, 1:526–530, 1988.

    Article  Google Scholar 

  18. H. A. Kierstead. A polynomial time approximation algorithm for dynamic storage allocation. Discrete Math., 88:231–237, 1991.

    Article  Google Scholar 

  19. H. A. Kierstead and K. Kolossa. On-line coloring of perfect graphs. To appear in Combinatorica.

    Google Scholar 

  20. H. A. Kierstead and S. G. Penrice. Recent results on a conjecture of Gyárfás. Congressus Numerantium, 79:182–186, 1990.

    Google Scholar 

  21. H. A. Kierstead and S. G. Penrice. Radius two trees specify χ-bounded classes. J. Graph Theory, 18:119–129, 1994.

    Google Scholar 

  22. H. A. Kierstead, S. G. Penrice, and W. T. Trotter. On-line graph coloring and recursive graph theory. Siam Journal on Discrete Math., 7:72–89, 1994.

    Google Scholar 

  23. H. A. Kierstead, S. G. Penrice, and W. T. Trotter. First-fit and on-line coloring of graphs which do not induce P 5. Siam Journal on Discrete Math., 8:485–498, 1995.

    Article  Google Scholar 

  24. H. A. Kierstead and J. Qin. Coloring interval graphs with First-Fit. Discrete Math., 144:47–57, 1995.

    Article  Google Scholar 

  25. H. A. Kierstead and W. T. Trotter. An extremal problem in recursive combinatorics. Congressus Numerantium, 33:143–153, 1981.

    Google Scholar 

  26. L. Lovász. Combinatorial Problems and Exercises. Akadémiai Kiadó, Budapest, 1993. Problem 13.13.

    Google Scholar 

  27. L. Lovász, M. Saks, and W. T. Trotter. An on-line graph coloring algorithm with sublinear performance ratio. Discrete Mathematics, 75:319–325, 1989.

    Google Scholar 

  28. A. B. Manaster and J. G. Rosenstein. Effective matchmaking (recursion theoretic aspects of a theorem of Philip Hall). Proc. Lond. Math. Soc., 25:615–654, 1972.

    Google Scholar 

  29. S. G. Penrice. On-line algorithms for ordered sets and comparability graphs. Preprint.

    Google Scholar 

  30. J. H. Schmerl. Private communication (1978).

    Google Scholar 

  31. J. H. Schmerl. Recursive colorings of graphs. Canad. J. Math., 32:821–830, 1980.

    Google Scholar 

  32. I. J. Stockmeyer. Private communication (1976).

    Google Scholar 

  33. D. P. Sumner. Subtrees of a graph and chromatic number. In Gary Chartrand, editor, The Theory and Applications of Graphs, pages 557–576. John Wiley & Sons, New York, 1981.

    Google Scholar 

  34. M. Szegedy. Private communication (1986).

    Google Scholar 

  35. E. Szemerédi. Private communication (1981).

    Google Scholar 

  36. S. Vishwanathan. Randomized on-line graph coloring. J. Algorithms, 13:657–669, 1992. Also in Proc. 31st IEEE Symposium on Foundations of Computer Science, 1990, 464–469.

    Google Scholar 

  37. D. R. Woodall. Problem no. 4, combinatorics. In T. P. McDonough and V. C. Marvon, editors, London Math. Soc. Lecture Note Series 13. Cambridge University Press, 1974. Proc. British Combinatorial Conference 1973.

    Google Scholar 

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Authors
  1. Hal A. Kierstead
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Amos Fiat Gerhard J. Woeginger

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© 1998 Springer-Verlag Berlin Heidelberg

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Kierstead, H.A. (1998). Coloring graphs on-line. In: Fiat, A., Woeginger, G.J. (eds) Online Algorithms. Lecture Notes in Computer Science, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029574

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  • DOI: https://doi.org/10.1007/BFb0029574

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  • Print ISBN: 978-3-540-64917-5

  • Online ISBN: 978-3-540-68311-7

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