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Coloring Powers of Graphs of Bounded Clique-Width

  • Ioan Todinca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2880)

Abstract

Given a graph G, the graph G l has the same vertex set and two vertices are adjacent in G l if and only if they are at distance at most l in G. The l-coloring problem consists in finding an optimal vertex coloring of the graph G l , where G the input graph. We show that, for any fixed value of l, the l-coloring problem is polynomial when restricted to graphs of bounded clique-width, if an expression of the graph is also part of the input.

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References

  1. 1.
    Bodlaender, H., Kratsch, D.: Private communication (2002)Google Scholar
  2. 2.
    Courcelle, B., Olariu, S.: Upper bounds to the clique-width of graphs. Discrete Applied Mathematics 101, 77–114 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Espelage, W., Gurski, F., Wanke, E.: How to solve NP-hard graph problems on clique-width bounded graphs in polynomial time. In: Brandstädt, A., Le, V.B. (eds.) WG 2001. LNCS, vol. 2204, pp. 117–128. Springer, Heidelberg (2001)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completness. Freeman, New York (1979)Google Scholar
  5. 5.
    Grigs, J.R., Yeh, R.K.: Labelling graphs with a condition at distance 2. SIAM J. on Discrete Math. 5, 586–595 (1992)CrossRefGoogle Scholar
  6. 6.
    Kobler, D., Rotics, U.: Polynomial algorithms for partitioning problems on graphs with fixed clique-width (extended abstract). In: Proceedings of the Twelfth Annual Symposium on Discrete Algorithms (SODA 2001), pp. 468–476 (2001)Google Scholar
  7. 7.
    Todinca, I.: Coloring powers of graphs of bounded clique-width. Research Report RR-2002-10, LIFO – Université d’Orléans (2002), http://www.univorleans.fr/SCIENCES/LIFO/prodsci/rapports/RR/RR2002/RR-2002-10.ps.gz
  8. 8.
    Zhou, X., Kanari, Y., Nishizeki, T.: Generalized vertex-colorings for partial k-trees. IEICE Trans. Fundamentals E83-A(4), 671–677 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ioan Todinca
    • 1
  1. 1.LIFO – Université d’OrléansOrléansFrance

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