Clique-Width is NP-Complete

@article{Fellows2009CliqueWidthIN,
  title={Clique-Width is NP-Complete},
  author={Michael R. Fellows and Frances A. Rosamond and Udi Rotics and Stefan Szeider},
  journal={SIAM J. Discret. Math.},
  year={2009},
  volume={23},
  pages={909-939}
}
Clique-width is a graph parameter that measures in a certain sense the complexity of a graph. Hard graph problems (e.g., problems expressible in monadic second-order logic with second-order quantification on vertex sets, which includes NP-hard problems such as 3-colorability) can be solved in polynomial time for graphs of bounded clique-width. We show that the clique-width of a given graph cannot be absolutely approximated in polynomial time unless $P = NP$. We also show that, given a graph $G… 

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