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Well-quasi-ordering Does Not Imply Bounded Clique-width

  • Vadim V. Lozin
  • Igor RazgonEmail author
  • Viktor Zamaraev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

We present a hereditary class of graphs of unbounded clique-width which is well-quasi-ordered by the induced subgraph relation. This result provides the negative answer to a question asked by Daligault, Rao and Thomassé in [3].

References

  1. 1.
    Atminas, A., Lozin, V.V., Razgon, I.: Well-quasi-ordering, tree-width and subquadratic properties of graphs. CoRR, abs/1410.3260 (2014)Google Scholar
  2. 2.
    Courcelle, B., Makowsky, J.A., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory Comput. Syst. 33(2), 125–150 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Daligault, J., Rao, M., Thomassé, S.: Well-quasi-order of relabel functions. Order 27(3), 301–315 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Damaschke, P.: Induced subgraphs and well-quasi-ordering. J. Graph Theor. 14(4), 427–435 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Diestel, R.: Graph Theory, 3rd edn. Springer-Verlag, Heidelberg (2005)zbMATHGoogle Scholar
  6. 6.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere!. Theor. Comput. Sci. 256(1–2), 63–92 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gurski, F., Wanke, E.: On the relationship between NLC-width and linear NLC-width. Theor. Comput. Sci. 347(1–2), 76–89 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–336 (1952)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Korpelainen, N., Lozin, V.V.: Two forbidden induced subgraphs and well-quasi-ordering. Discrete Math. 311(16), 1813–1822 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kruskal, J.B.: The theory of well-quasi-ordering: a frequently discovered concept. J. Comb. Theory Ser. A 13(3), 297–305 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lozin, V.V., Rautenbach, D.: The relative clique-width of a graph. J. Comb. Theory Ser. B 97(5), 846–858 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Petkovsek, M.: Letter graphs and well-quasi-order by induced subgraphs. Discrete Math. 244(1–3), 375–388 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Robertson, N., Seymour, P.D.: Graph minors XX. Wagner’s conjecture. J. Comb. Theory Ser. B 92(2), 325–357 (2004)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of Computer Science and Information SystemsBirkbeck, University of LondonLondonUK
  3. 3.Mathematics InstituteUniversity of WarwickCoventryUK

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