International Symposium on Mathematical Foundations of Computer Science

MFCS 2015: Mathematical Foundations of Computer Science 2015 pp 139-150 | Cite as

Bounding the Clique-Width of H-free Chordal Graphs

  • Andreas Brandstädt
  • Konrad K. Dabrowski
  • Shenwei Huang
  • Daniël Paulusma
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)

Abstract

A graph is H-free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique-width. Brandstädt, Le and Mosca erroneously claimed that the gem and the co-gem are the only two 1-vertex \(P_4\)-extensions H for which the class of H-free chordal graphs has bounded clique-width. In fact we prove that bull-free chordal and co-chair-free chordal graphs have clique-width at most 3 and 4, respectively. In particular, we prove that the clique-width is:
  1. (i)

    bounded for four classes of H-free chordal graphs;

     
  2. (ii)

    unbounded for three subclasses of split graphs.

     

Our main result, obtained by combining new and known results, provides a classification of all but two stubborn cases, that is, with two potential exceptions we determine all graphs H for which the class of H-free chordal graphs has bounded clique-width. We illustrate the usefulness of this classification for classifying other types of graph classes by proving that the class of \((2P_1+ P_3, K_4)\)-free graphs has bounded clique-width via a reduction to \(K_4\)-free chordal graphs. Finally, we give a complete classification of the (un)boundedness of clique-width of H-free weakly chordal graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andreas Brandstädt
    • 1
  • Konrad K. Dabrowski
    • 2
  • Shenwei Huang
    • 3
  • Daniël Paulusma
    • 2
  1. 1.Institute of Computer ScienceUniversität RostockRostockGermany
  2. 2.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  3. 3.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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