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The vertex separation number of a graph equals its path-width. (English) Zbl 0764.68121
Summary: We show that the problem of finding a graph’s vertex separation number and path-width are the same. The equivalence of these problems with the gate matrix layout and the node search number problems then follows immediately from the results of M. R. Fellows and M. A. Langston and M. Kirousis and C. H. Papadimitriou, respectively. The fixed parameter variants of problems are known to possess $$O(n^ 2)$$ decision algorithms based on finite but unknown obstruction sets. We show how all tree obstructions in these sets may be constructively obtained.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 68Q25 Analysis of algorithms and problem complexity 68R05 Combinatorics in computer science
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##### References:
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