Block-Graph Width

  • Maw-Shang Chang
  • Ling-Ju Hung
  • Ton Kloks
  • Sheng-Lung Peng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5532)


The \(\mathcal{G}\)-width of a class of graphs \(\mathcal{G}\) is defined as follows. A graph G has \(\mathcal{G}\)-width k if there are k independent sets \(\mathbb{N}_1,\dots,\mathbb{N}_{\rm \tt k}\) in G such that G can be embedded into a graph \({\rm H \in \mathcal{G}}\) such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in ℕi. For the class \(\mathfrak{B}\) of block graphs we show that \(\mathfrak{B}\)-width is NP-complete and we present fixed-parameter algorithms.


Decomposition Tree Chordal Graph Graph Class Block Graph Induce Subgraph 
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  1. 1.
    Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph classes: A survey. In: SIAM Monographs on Discrete Mathematics and Applications, Philadelphia (1999)Google Scholar
  2. 2.
    Chang, M.-S., Hsieh, S.-Y., Chen, G.-H.: Dynamic programming on distance-hereditary graphs. In: Leong, H.-V., Jain, S., Imai, H. (eds.) ISAAC 1997. LNCS, vol. 1350, pp. 344–353. Springer, Heidelberg (1997)Google Scholar
  3. 3.
    Courcelle, B., Oum, S.: Vertex minors, monadic second-order logic, and a conjecture by Seese. Journal of Combinatorial Theory, Series B 97, 91–126 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Golumbic, M.C., Kaplan, H., Shamir, R.: Graph sandwich problems. Journal of Algorithms 19, 449–473 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 2, 326–336 (1952)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hliněný, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Computer Journal 51, 326–362 (2008)CrossRefGoogle Scholar
  7. 7.
    Kay, D.C., Chartrand, G.: A characterization of certain ptolemaic graphs. Canadian Journal of Mathematics 17, 342–346 (1965)zbMATHMathSciNetGoogle Scholar
  8. 8.
    McMorris, F.R., Wang, C., Zhang, P.: On probe interval graphs. Discrete Applied Mathematics 88, 315–324 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Orlin, J.: Contentment in graph theory: covering graphs with cliques. Indagationes Mathematicae 39, 406–424 (1977)MathSciNetGoogle Scholar
  10. 10.
    Oum, S.: Rank–width and vertex–minors. Journal of Combinatorial Theory, Series B 95, 79–100 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Oum, S.: Graphs of bounded rank-width. PhD Thesis. Princeton University, Princeton (2005)Google Scholar
  12. 12.
    Petkovšek, M.: Letter graphs and well-quasi-order by induced subgraphs. Discrete Mathematics 244, 375–388 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Tarjan, R.: Depth-first search and linear graph algorithms. SIAM Journal of Computing 1, 146–160 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Zhang, P., Schon, E.A., Fischer, S.G., Cayanis, E., Weiss, J., Kistler, S., Bourne, P.E.: An algorithm based on graph theory for the assembly of contigs in physical mapping of DNA. CABIOS 10, 309–317 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Maw-Shang Chang
    • 1
  • Ling-Ju Hung
    • 1
  • Ton Kloks
    • 3
  • Sheng-Lung Peng
    • 2
  1. 1.Department of Computer Science and Information EngineeringNational Chung Cheng UniversityTaiwan
  2. 2.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityShoufeng, HualienTaiwan
  3. 3.No Affiliations 

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