On the Relationship between Clique-Width and Treewidth

(Extended abstract)
  • Derek G. Corneil
  • Udi Rotics
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2204)

Abstract

Treewidth is generally regarded as one of the most useful parameterizations of a graph’s construction. Clique-width is a similar parameterizations that shares one of the powerful properties of treewidth, namely: if a graph is of bounded treewidth (or clique-width), then there is a polynomial time algorithm for any graph problem expressible in Monadic Second Order Logic, using quantifiers on vertices (in the case of clique-width you must assume a clique-width parse expression is given). In studying the relationship between treewidth and clique-width, Courcelle and Olariu showed that any graph of bounded treewidth is also of bounded clique-width; in particular, for any graph G with treewidth k, the clique-width of G ≤ 4 * 2k−1 + 1.

In this paper, we improve this result to the clique-width of G ≤ 3 * 2k−1 and more importantly show that there is an exponential lower bound on this relationship. In particular, for any k, there is a graph G with treewidth = k where the clique-width of G ≥ 2[k/2]−1.

Keywords

Polynomial Time Algorithm Construction Tree Order Logic Interval Graph Parse Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Derek G. Corneil
    • 1
  • Udi Rotics
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCanada
  2. 2.School of Mathematics and Computer ScienceNetanya Academic CollegeNetanyaIsrael

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