Edge Clique Partition of K4-Free and Planar Graphs

  • Rudolf Fleischer
  • Xiaotian Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


Edge k -Clique Partition k -ECP is the problem of dividing the edge set of an undirected graph into a set of at most k edge-disjoint cliques, where k ≥ 1 is an input parameter. The problem is NP-hard but in FPT. We propose several improved FPT algorithms for k -ECP on K 4-free graphs, planar graphs, and cubic graphs.


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  1. 1.
    Alber, J., Fernau, H., Niedermeier, R.: Graph separators: a parameter view. Journal of Computer and System Sciences 67, 808–832 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alon, N., Yuster, R., Zwick, U.: Color-coding. Journal of the ACM 42(4), 844–856 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bodlaender, H.L., Fellows, M.R., Heggernes, P., Mancini, F., Papadopoulos, C., Rosamond, F.: Clustering with partial information. Theoretical Computer Science 411(7-9), 1202–1211 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cerioli, M.R., Faria, L., Ferreira, T.O., Martinhon, C.A.J., Protti, F., Reed, B.: Partition into cliques for cubic graphs: planar case, complexity and approximation. Discrete Applied Mathematics 156, 2270–2278 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Demaine, E.D., Fomin, F.V., Hajiaghayi, M., Thilikos, D.M.: Subexponential parametrized algorithms on bounded-genus graphs and h-minor-free graphs. Journal of the ACM 52(6), 866–893 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Djidjev, H.N., Venkatesan, S.M.: Reduced constants for simple cycle graph separation. Acta Informatica 34, 231–243 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  8. 8.
    Fellows, M.R., Knauer, C., Nishimura, N., Ragde, P., Rosamond, F., Stege, U., Thilikos, D.M., Whitesides, S.: Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 311–322. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Figueroa, A., Bornemann, J., Jiang, T.: Clustering binary fingerprint vectors with missing values for DNA array data analysis. Journal of Computational Biology 11, 887–901 (2004)CrossRefGoogle Scholar
  10. 10.
    Fisher, D.: The number of triangles in a K 4-free graph. Discrete Mathematics 69, 203–205 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fomin, F.V., Golovach, P., Thilikos, D.M.: Contraction Bidimensionality: The Accurate Picture. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 706–717. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Holyer, I.: The NP-completeness of some edge-partition problems. SIAM Journal on Computing 10(4), 713–717 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Mathieson, L., Prieto, E., Shaw, P.: Packing edge disjoint triangles: A parameterized view. In: Downey, R.G., Fellows, M.R., Dehne, F. (eds.) IWPEC 2004. LNCS, vol. 3162, pp. 127–137. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Mujuni, E., Rosamond, F.: Parameterized complexity of the clique partition problem. In: Proceedings of the 14th Computing: Australian Theory Symposium (CATS 2008), Conferences in Research and Practice in Information Technology, vol. 77, pp. 75–78 (2008)Google Scholar
  15. 15.
    Niedermeier, R.: Invitation to fixed parameter algorithms. Oxford University Press, U.K (2006)CrossRefzbMATHGoogle Scholar
  16. 16.
    Niedermeier, R., Rossmanith, P.: Upper Bounds for Vertex Cover Further Improved. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 561–570. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Orlin, J.: Contentment in graph theory: covering graphs with cliques. Indagationed Mathematicae 39, 406–424 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Schmidt, J.P., Siegel, A.: The spatial complexity of oblivious k-probe hash functions. SIAM Journal on Computing 19(5), 775–786 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Shaohan, M., Wallis, W.D., Lin, W.J.: The complexity of the clique partition number problem. Congressus Numerantium 67, 56–66 (1988); Proceedings of the 19th Southeastern Conference on Combinatorics, Graph Theory and ComputingMathSciNetzbMATHGoogle Scholar
  20. 20.
    Wu, X., Lin, Y., Fleischer, R.: Research of fixed parameter algorithm for clique partition problem. Computer Engineering 37(11), 92–93 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  • Xiaotian Wu
    • 1
  1. 1.School of CS and IIPLFudan UniversityShanghaiChina

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