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- W1518448510 abstract "Let $H$ be a fixed graph. What can be said about graphs $G$ that have no subgraph isomorphic to a subdivision of $H$? Grohe and Marx proved that such graphs $G$ satisfy a certain structure theorem that is not satisfied by graphs that contain a subdivision of a (larger) graph $H_1$. Dvořak found a clever strengthening---his structure is not satisfied by graphs that contain a subdivision of a graph $H_2$, where $H_2$ has embedding as $H$. Building upon Dvořak's theorem, we prove that said graphs $G$ satisfy a similar structure theorem. Our structure is not satisfied by graphs that contain a subdivision of a graph $H_3$ that has similar embedding properties as $H$ and has the same maximum degree as $H$. This will be important in a forthcoming application to well-quasi-ordering." @default.
- W1518448510 created "2016-06-24" @default.
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- W1518448510 date "2014-07-16" @default.
- W1518448510 modified "2023-09-27" @default.
- W1518448510 title "Excluding subdivisions of bounded degree graphs." @default.
- W1518448510 hasPublicationYear "2014" @default.
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