Parameterized complexity of coloring problems: Treewidth versus vertex cover

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5532 LNCS, Issue , 2009, Pages 221-230

  Fiala, Jiří ^a   Golovach, Petr A ^b   Kratochv́il, Jan ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL ASSIGNMENT; COLORING PROBLEMS; EQUITABLE COLORING; FIXED-PARAMETER COMPLEXITY; LIST COLORING; PARAMETERIZED; PARAMETERIZED COMPLEXITY; PARAMETRIZATION; PRECOLORING EXTENSION; TREE-WIDTH; VERTEX COVER;

LABELS;

COLORING;

EID: 67650229853     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02017-9_25     Document Type: Conference Paper

References (23)

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).
2. Agnarsson, G., Halldórsson, M.M.: Coloring powers of planar graphs. SIAM J. Discrete Math. 16, 651-662 (2003) (electronic).
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).
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).
5. Bodlaender, H.L., Fomin, F.V.: Equitable colorings of bounded treewidth graphs. Theoret. Comput. Sci. 349, 22-30 (2005).
6. Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J. 51, 255-269 (2008).
7. Calamoneri, T.: The l(h, k)-labelling problem: A survey and annotated bibliography. Comput. J. 49, 585-608 (2006).
8. Chang, G.J., Kuo, D.: The L(2, 1)-labeling problem on graphs. SIAM J. Discrete Math. 9, 309-316 (1996).
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).
10. Downey, R.G., Fellows, M.R.: Parameterized complexity. Monographs in Computer Science. Springer, New York (1999).
11. Dvořák, Z., Král, D., Nejedlý, P., Škrekovski, R.: Coloring squares of planar graphs with girth six. European J. Combin. 29, 838-849 (2008).
12. Fellows, M., Lokshtanov, D., Misra, N., Rosamond, F.A., Saurabh, S.: Graph layout problems parameterized by vertex cover. In: ISAAC (2008).
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. LNCS, vol. 4616, pp. 366-377. Springer, Heidelberg (2007).
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).
15. Fiala, J., Golovach, P.A., Kratochvíl, J.: Computational complexity of the distance constrained labeling problem for trees (extended abstract). In: Aceto, L., Damgåard, 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).
16. Frank, A., Tardos, É.: An application of simultaneous Diophantine approximation in combinatorial optimization. Combinatorica 7, 49-65 (1987).
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).
18. Kannan, R.: Minkowski's convex body theorem and integer programming. Math. Oper. Res. 12, 415-440 (1987).
19. Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Math. Oper. Res. 8, 538-548 (1983).
20. McDiarmid, C., Reed, B.: Channel assignment on graphs of bounded treewidth. Discrete Math. 273, 183-192 (2003); EuroComb 2001 (Barcelona).
21. Tuza, Z.: Graph colorings with local constraints-a survey. Discuss. Math. Graph Theory 17, 161-228 (1997).
22. Yeh, R.K.: A survey on labeling graphs with a condition at distance two. Discrete Math. 306, 1217-1231 (2006).
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).