# Dynamic algorithms for graphs with treewidth 2

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## Abstract

In this paper, we consider algorithms for maintaining treedecompositions with constant bounded treewidth under edge and vertex insertions and deletions for graphs with treewidth at most 2 (also called: partial 2-trees, or series-parallel graphs), and for almost trees with parameter *k*. Each operation can be performed in *O*(log *n*) time. For a large number of graph decision, optimization and counting problems, information can be maintained using *O*(log *n*) time per update, such that queries can be resolved in *O*(log *n*) or *O*(1) time. Similar results hold for the classes of almost trees with parameter *k*, for fixed *k*.

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© Springer-Verlag Berlin Heidelberg 1994