Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover

(Extended Abstract)
  • Jiří Fiala
  • Petr A. Golovach
  • Jan Kratochvíl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


We compare the fixed parameter complexity of various variants of coloring problems (including List Coloring, Precoloring Extension, Equitable Coloring, L(p,1)-Labeling and Channel Assignment) when parameterized by treewidth and by vertex cover number. In most (but not all) cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems.


Parameterized Complexity Channel Assignment Vertex Cover Distance Power Graph Coloring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aardal, K., Weismantel, R., Wolsey, L.A.: Non-standard approaches to integer programming. Discrete Appl. Math. 123, 5–74 (2002); Workshop on Discrete Optimization, DO 1999, Piscataway, NJ (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Agnarsson, G., Halldórsson, M.M.: Coloring powers of planar graphs. SIAM J. Discrete Math. 16, 651–662 (2003) (electronic)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Alon, N.: Restricted colorings of graphs, in Surveys in combinatorics, 1993 (Keele). London Math. Soc. Lecture Note Ser., vol. 187, pp. 1–33. Cambridge Univ. Press, Cambridge (1993)Google Scholar
  4. 4.
    Bodlaender, H.L.: Treewidth: Characterizations, applications, and computations. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 1–14. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Bodlaender, H.L., Fomin, F.V.: Equitable colorings of bounded treewidth graphs. Theoret. Comput. Sci. 349, 22–30 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J. 51, 255–269 (2008)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Calamoneri, T.: The l(h, k)-labelling problem: A survey and annotated bibliography. Comput. J. 49, 585–608 (2006)CrossRefGoogle Scholar
  8. 8.
    Chang, G.J., Kuo, D.: The L(2,1)-labeling problem on graphs. SIAM J. Discrete Math. 9, 309–316 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Dom, M., Lokshtanov, D., Saurabh, S., Villanger, Y.: Capacitated domination and covering: A parameterized perspective. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 78–90. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999)Google Scholar
  11. 11.
    Dvořák, Z., Král, D., Nejedlý, P., Škrekovski, R.: Coloring squares of planar graphs with girth six. European J. Combin. 29, 838–849 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Fellows, M., Lokshtanov, D., Misra, N., Rosamond, F.A., Saurabh, S.: Graph layout problems parameterized by vertex cover. In: ISAAC (2008)Google Scholar
  13. 13.
    Fellows, M.R., Fomin, F.V., Lokshtanov, D., Rosamond, F.A., Saurabh, S., Szeider, S., Thomassen, C.: On the complexity of some colorful problems parameterized by treewidth. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA 2007. LNCS, vol. 4616, pp. 366–377. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Fiala, J., Golovach, P.A., Kratochvíl, J.: Distance constrained labelings of graphs of bounded treewidth. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 360–372. Springer, Heidelberg (2005)Google Scholar
  15. 15.
    Fiala, J., Golovach, P.A., Kratochvíl, J.: Computational complexity of the distance constrained labeling problem for trees (extended abstract). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 294–305. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Frank, A., Tardos, É.: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7, 49–65 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Golovach, P.A.: Systems of pairs of q-distant representatives, and graph colorings. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 293, 5–25, 181 (2002)Google Scholar
  18. 18.
    Kannan, R.: Minkowski’s convex body theorem and integer programming. Math. Oper. Res. 12, 415–440 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8, 538–548 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    McDiarmid, C., Reed, B.: Channel assignment on graphs of bounded treewidth. Discrete Math. 273, 183–192 (2003); EuroComb 2001 (Barcelona)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Tuza, Z.: Graph colorings with local constraints—a survey. Discuss. Math. Graph Theory 17, 161–228 (1997)zbMATHMathSciNetGoogle Scholar
  22. 22.
    Yeh, R.K.: A survey on labeling graphs with a condition at distance two. Discrete Math. 306, 1217–1231 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Zhou, X., Kanari, Y., Nishizeki, T.: Generalized vertex-coloring of partial k-trees. IEICE Trans. Fundamentals of Electronics, Communication and Computer Sciences E83-A, 671–678 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jiří Fiala
    • 1
  • Petr A. Golovach
    • 2
  • Jan Kratochvíl
    • 1
  1. 1.Institute for Theoretical Computer Science, and Department of Applied MathematicsCharles UniversityPragueCzech Republic
  2. 2.Institutt for informatikkUniversitetet i BergenNorway

Personalised recommendations