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After the number of vertices, Vertex Cover is the largest of the classicalgraph parameters and has more and more frequently been used as a separateparameter in parameterized problems, including problems that are not directlyrelated to the Vertex Cover. Here we consider the TREEWIDTH and PATHWIDTHproblems parameterized by k, the size of a minimum vertex cover of the inputgraph. We show that the PATHWIDTH and TREEWIDTH can be computed in O*(3^k)time. This complements recent polynomial kernel results for TREEWIDTH andPATHWIDTH parameterized by the Vertex Cover.

TREEWIDTH and PATHWIDTH parameterized by vertex cover