On the OBDD Size for Graphs of Bounded Tree- and Clique-Width

  • Klaus Meer
  • Dieter Rautenbach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


We study the size of OBDDs (ordered binary decision diagrams) for representing the adjacency function f G of a graph G on n vertices. Our results are as follows:

-) For graphs of bounded tree-width there is an OBDD of size O(logn) for f G that uses encodings of size O(logn) for the vertices;

-) For graphs of bounded clique-width there is an OBDD of size O(n) for f G that uses encodings of size O(n) for the vertices;

-) For graphs of bounded clique-width such that there is a reduced term for G (to be defined below) that is balanced with depth O(logn) there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices;

-) For cographs, i.e. graphs of clique-width at most 2, there is an OBDD of size O(n) for f G that uses encodings of size O(logn) for the vertices. This last result improves a recent result by Nunkesser and Woelfel [14].


Boolean Function Tree Decomposition Binary Decision Diagram Adjacency List Discrete Apply Mathematic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Klaus Meer
    • 1
  • Dieter Rautenbach
    • 2
  1. 1.Department of Mathematics and Computer ScienceSyddansk UniversitetOdense MDenmark
  2. 2.Forschungsinstitut für Diskrete MathematikUniversität BonnBonnGermany

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