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On a disparity between relative cliquewidth and relative NLC-width

Haiko Müller, Ruth Urner
2010 Discrete Applied Mathematics  
Many hard problems on graphs become solvable in polynomial-time if the inputs are restricted to graphs of bounded clique-or NLC-width. Cliquewidth and NLC-width differ at most by a factor of two.  ...  Cliquewidth and NLC-width are two closely related parameters that measure the complexity of graphs.  ...  Theorem 1 . 1 The relative NLC-width of a graph on n vertices can be computed in time O(n 3 ) while the problem Relative Cliquewidth is NP-complete.  ... 
doi:10.1016/j.dam.2009.06.024 fatcat:7oldbulk6bfjbeqpq7ddtqlcf4