Journal of Mathematical Sciences

, Volume 126, Issue 3, pp 1141–1151 | Cite as

Systems of pairs of q-distant representatives, and graph colorings

  • P. A. Golovach


The NP-completeness of a number of graph coloring problems related to the frequency assignment problem is proved. For this purpose, we introduce problems concerning systems of pairs of q-distant representatives (which are related to the well-known problem about the system of distinct representatives, but are NP-complete for q ≥ 2), which turned out to be convenient for proving the NP-completeness of various graph coloring problems. Bibliography: 11 titles.


Assignment Problem Graph Coloring Coloring Problem Frequency Assignment Graph Coloring Problem 
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  1. 1.
    M. R. Garey and D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, San Francisco (1979).Google Scholar
  2. 2.
    R. Battiti, A. A. Bertossi, and M. A. Bonuccelli, “Assigning codes in wireless network:Bounds and scaling properties,” Wireless Networks, 5, No. 3, 195–209 (1999).Google Scholar
  3. 3.
    H. L. Bodlaender, T. Kloks, R. B. Tan, and J. Leeuwen, “Approximation for λ-coloring of graphs,” Lect. Notes Comput. Sci., 1770, 395–409 (2000).Google Scholar
  4. 4.
    G. J. Chang and D. Kuo, “The L(2, 1)-labeling problem on graphs,” SIAM J. Discrete Math., 9, 309–316 (1996).Google Scholar
  5. 5.
    J. Fiala, J. Kratochvil, and A. Proskurowski, “Distance constrained labeling of precoloed trees,” Lect. Notes Comput. Sci., 2202, 285–292 (2001).Google Scholar
  6. 6.
    J. Fiala, T. Kloks, and J. Kratochvil, “Fixed-parameter complexity of λ-coloring,” Discrete Appl. Math., 113, 59–72 (2001).Google Scholar
  7. 7.
    D. Fotakis, G. Pantziou, G. Pentaris, and P. Spirakis, “Frequency assignment in mobile and radio networks,” Networks in distributed computing, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 45 (1997), pp. 73–90.Google Scholar
  8. 8.
    J. P. Georges and D. W. Mauro, “On the size of graphs labeled with a condition at distance two,” J. Graph Theory, 22, 47–57 (1996).Google Scholar
  9. 9.
    J. R. Griggs and R. K. Yeh, “Labelling graphs with a condition at distance 2,” SIAM J. Discrete Math., 5, 586–595 (1992).Google Scholar
  10. 10.
    R. A. Murphey, P. M. Pardalos, and M. G. Resende, “Frequency assignment problems,” AT&T Labs Research Technical Report 98. 16. 1.Google Scholar
  11. 11.
    D. D.-F. Liu and R. K. Yeh, “On distance two labelling of graphs,” Ars Combin., 47, 13–22 (1997).Google Scholar

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© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. A. Golovach

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