Problems easy for tree-decomposable graphs extended abstract

  • Stefan Arnborg
  • Jens Lagergren
  • Detlef Seese
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


Using a variation of the interpretability concept we show that all graph properties definable in monadic second order logic (MS properties) with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded tree-width, giving an alternative proof of a recent result by Courcelle. We allow graphs with directed and/or undirected edges, labeled on edges and/or vertices with labels taken from a finite set. We extend MS properties to Extended Monadic Second-order (EMS) problems involving counting or summing evaluations given with the graph over sets definable in monadic second order logic. Our tecnique allowes us to solve also some EMS problems in linear time or in polynomial or pseudopolynomial time for classes of graphs of fixed bounded tree-width. Most problems for wich linear time algorithms for graphs of bounded tree width where previously known to exist, and many others, are EMS problems.


Linear Time Binary Tree Order Logic Undirected Edge Tree Automaton 
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 1988

Authors and Affiliations

  • Stefan Arnborg
    • 1
  • Jens Lagergren
    • 1
  • Detlef Seese
    • 2
  1. 1.Department of Numerical Analysis and Computing ScienceThe Royal Institute of TechnologyStockholmSweden
  2. 2.Karl-Weierstrass-Institut für MathematikAkademie der Wissenschaften der DDRBerlinDDR

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