Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clique-Width: Harnessing the Power of Atoms   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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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph