From Tree-Width to Clique-Width: Excluding a Unit Interval Graph

  • Vadim V. Lozin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


From the theory of graph minors we know that the class of planar graphs is the only critical class with respect to tree-width. In the present paper, we reveal a critical class with respect to clique-width, a notion generalizing tree-width. This class is known in the literature under different names, such as unit interval, proper interval or indifference graphs, and has important applications in various fields, including molecular biology. We prove that the unit interval graphs constitute a minimal hereditary class of unbounded clique-width. As an application, we show that list coloring is fixed parameter tractable in the class of unit interval graphs.


Tree-width Clique-width Unit interval graphs Fixed parameter tractability 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vadim V. Lozin
    • 1
  1. 1.DIMAP and Mathematics InstituteUniversity of WarwickCoventryUK

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