Linear Clique-Width of Bi-complement Reducible Graphs

  • Bogdan Alecu
  • Vadim LozinEmail author
  • Viktor Zamaraev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)


We prove that in the class of bi-complement reducible graphs linear clique-width is unbounded and show that this class contains exactly two minimal hereditary subclasses of unbounded linear clique-width.



Viktor Zamaraev acknowledges support from EPSRC, grant EP/P020372/1.


  1. 1.
    Adler, I., Kanté, M.M.: Linear rank-width and linear clique-width of trees. Theoret. Comput. Sci. 589, 87–98 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brandstädt, A., Dabrowski, K.K., Huang, S., Paulusma, D.: Bounding the clique-width of \(H\)-free split graphs. Discrete Appl. Math. 211, 30–39 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Brignall, R., Korpelainen, N., Vatter, V.: Linear clique-width for hereditary classes of cographs. J. Graph Theory 84, 501–511 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Collins, A., Foniok, J., Korpelainen, N., Lozin, V., Zamaraev, V.: Infinitely many minimal classes of graphs of unbounded clique-width. Discrete Appl. Math. (accepted).
  5. 5.
    Dabrowski, K.K., Huang, S., Paulusma, D.: Classifying the clique-width of \(H\)-free bipartite graphs. Discrete Appl. Math. 200, 43–51 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fellows, M.R., Rosamond, F.A., Rotics, U., Szeider, S.: Clique-width is NP-complete. SIAM J. Discrete Math. 23(2), 909–939 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Giakoumakis, V., Vanherpe, J.: Bi-complement reducible graphs. Adv. Appl. Math. 18, 389–402 (1997)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Golumbic, M.C.: Trivially perfect graphs. Discrete Math. 24, 105–107 (1978)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gurski, F., Wanke, E.: On the relationship between NCL-width and linear NCL-width. Theoret. Comput. Sci. 347, 76–89 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Heggernes, P., Meister, D., Papadopoulos, C.: Graphs of linear clique-width at most 3. Theoret. Comput. Sci. 412, 5466–5486 (2011)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Heggernes, P., Meister, D., Papadopoulos, C.: Characterising the linear clique-width of a class of graphs by forbidden induced subgraphs. Discrete Appl. Math. 160, 888–901 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lozin, V.: Minimal classes of graphs of unbounded clique-width. Ann. Comb. 15, 707–722 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lozin, V., Rautenbach, D.: Chordal bipartite graphs of bounded tree- and clique-width. Discrete Math. 283, 151–158 (2004)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Lozin, V.V., Volz, J.: The clique-width of bipartite graphs in monogenic classes. Int. J. Found. Comput. Sci. 19, 477–494 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yan, J.-H., Chen, J.-J., Chang, G.J.: Quasi-threshold graphs. Discrete Appl. Math. 69, 247–255 (1996)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of Computer ScienceDurham UniversityDurhamUK

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