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- W4387389923 abstract "A class $mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $mathcal{G}^mathrm{apex}$ the class of graphs $G$ that contain a vertex $v$ such that $G-v$ is in $mathcal{G}$. We prove that if a hereditary class $mathcal{G}$ has finitely many forbidden induced subgraphs, then so does $mathcal{G}^mathrm{apex}$. The hereditary class of cographs consists of all graphs $G$ that can be generated from $K_1$ using complementation and disjoint union. A graph is an apex cograph if it contains a vertex whose deletion results in a cograph. Cographs are precisely the graphs that do not have the $4$-vertex path as an induced subgraph. Our main result finds all such forbidden induced subgraphs for the class of apex cographs." @default.
- W4387389923 created "2023-10-06" @default.
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- W4387389923 date "2023-10-03" @default.
- W4387389923 modified "2023-10-07" @default.
- W4387389923 title "Apex Graphs and Cographs" @default.
- W4387389923 doi "https://doi.org/10.48550/arxiv.2310.02551" @default.
- W4387389923 hasPublicationYear "2023" @default.
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