Computing Bounded Path Decompositions in Logspace

We present a logspace algorithm to compute path decompositions of bounded pathwidth graphs, thus settling its complexity. Prior to our work, the best known upper bound to compute such decompositions was linear time [Bod96, BK96]. We also show that deciding if the pathwidth of a graph is at most a given constant is L-complete. Besides being of fundamental interest, our results represent an important step to gain a better understanding of the complexity of Graph Isomorphism of bounded pathwidth graphs.

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