Linear Clique-Width for Hereditary Classes of Cographs

@article{Brignall2017LinearCF,
  title={Linear Clique-Width for Hereditary Classes of Cographs},
  author={Robert Brignall and Nicholas Korpelainen and Vincent Vatter},
  journal={J. Graph Theory},
  year={2017},
  volume={84},
  pages={501-511}
}
The class of cographs is known to have unbounded linear clique-width. We prove that a hereditary class of cographs has bounded linear clique-width if and only if it does not contain all quasi-threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes. 

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