A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth

  • Authors:
  • Hans L. Bodlaender

  • Affiliations:
  • -

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1996

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Abstract

In this paper, we give for constant $k$ a linear-time algorithm that, given a graph $G=(V,E)$, determines whether the treewidth of $G$ is at most $k$ and, if so, finds a tree-decomposition of $G$ with treewidth at most $k$. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear-time recognition algorithm. Another consequence is that a similar result holds when we look instead for path-decompositions with pathwidth at most some constant $k$.