Abstract
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.
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References
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)
Agnarsson, G., Halldórsson, M.M.: Coloring powers of planar graphs. SIAM J. Discrete Math. 16, 651–662 (2003) (electronic)
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)
Bodlaender, H.L.: Treewidth: Characterizations, applications, and computations. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 1–14. Springer, Heidelberg (2006)
Bodlaender, H.L., Fomin, F.V.: Equitable colorings of bounded treewidth graphs. Theoret. Comput. Sci. 349, 22–30 (2005)
Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J. 51, 255–269 (2008)
Calamoneri, T.: The l(h, k)-labelling problem: A survey and annotated bibliography. Comput. J. 49, 585–608 (2006)
Chang, G.J., Kuo, D.: The L(2,1)-labeling problem on graphs. SIAM J. Discrete Math. 9, 309–316 (1996)
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)
Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999)
Dvořák, Z., Král, D., Nejedlý, P., Škrekovski, R.: Coloring squares of planar graphs with girth six. European J. Combin. 29, 838–849 (2008)
Fellows, M., Lokshtanov, D., Misra, N., Rosamond, F.A., Saurabh, S.: Graph layout problems parameterized by vertex cover. In: ISAAC (2008)
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)
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)
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)
Frank, A., Tardos, É.: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7, 49–65 (1987)
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)
Kannan, R.: Minkowski’s convex body theorem and integer programming. Math. Oper. Res. 12, 415–440 (1987)
Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8, 538–548 (1983)
McDiarmid, C., Reed, B.: Channel assignment on graphs of bounded treewidth. Discrete Math. 273, 183–192 (2003); EuroComb 2001 (Barcelona)
Tuza, Z.: Graph colorings with local constraints—a survey. Discuss. Math. Graph Theory 17, 161–228 (1997)
Yeh, R.K.: A survey on labeling graphs with a condition at distance two. Discrete Math. 306, 1217–1231 (2006)
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)
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Fiala, J., Golovach, P.A., Kratochvíl, J. (2009). Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover . In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_25
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DOI: https://doi.org/10.1007/978-3-642-02017-9_25
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