Clique-Width: Harnessing the Power of Atoms

@article{Dabrowski2020CliqueWidthHT,
  title={Clique-Width: Harnessing the Power of Atoms},
  author={Konrad K. Dabrowski and Tom{\'a}{\vs} Masař{\'i}k and Jana Novotn{\'a} and Dani{\"e}l Paulusma and Paweł Rzaͅżewski},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.03578}
}
Many NP-complete graph problems are polynomially solvable on graph classes of bounded clique-width. Several of these problems are polynomially solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of G. Hence, we initiate a systematic study into boundedness of clique-width of atoms of hereditary graph classes. A graph G is H-free if H is not an induced subgraph of G, and G is (H_1, H_2)-free if it is both H_1-free and H_2-free. A class of H-free… 

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