A simple linear-time algorithm for finding path-decompositions of small width

Mathematics – Combinatorics

Scientific paper

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9 pages

Scientific paper

We described a simple algorithm running in linear time for each fixed
constant $k$, that either establishes that the pathwidth of a graph $G$ is
greater than $k$, or finds a path-decomposition of $G$ of width at most
$O(2^{k})$. This provides a simple proof of the result by Bodlaender that many
families of graphs of bounded pathwidth can be recognized in linear time.

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