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arXiv · 2006.03578

Clique-Width: Harnessing the Power of Atoms

Konrad K. Dabrowski·Tomáš Masařík·Jana Novotná·Daniël Paulusma·Paweł Rzążewski
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Abstract

Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class ${\cal G}$ if they are so on the atoms (graphs with no clique cut-set) of ${\cal G}$. 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 it is $(H_1,H_2)$-free if it is both $H_1$-free and $H_2$-free. A class of $H$-free graphs has bounded clique-width if and only if its atoms have this property. This is no longer true for $(H_1,H_2)$-free graphs, as evidenced by one known example. We prove the existence of another such pair $(H_1,H_2)$ and classify the boundedness of clique-width on $(H_1,H_2)$-free atoms for all but 18 cases.

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BibTeXRIS

Konrad K. Dabrowski, Tomáš Masařík, Jana Novotná, Daniël Paulusma, Paweł Rzążewski. 2020-06-05. Clique-Width: Harnessing the Power of Atoms. https://doi.org/10.1002/jgt.23000 10.1007/978-3-030-60440-0_10

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