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- W4226148049 abstract "The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs in open. The complexities of recognising many subclasses of SOGs are known. We consider several subclasses of SOGs by restricting the underlying tree. For a fixed integer $k geq 3$, we consider: begin{my_itemize} item The overlap graphs of subtrees in a tree where that tree has $k$ leaves item The overlap graphs of subtrees in trees that can be derived from a given input tree by subdivision and have at least 3 leaves item The overlap and intersection graphs of paths in a tree where that tree has maximum degree $k$ end{my_itemize} We show that the recognition problems of these classes are NP-complete. For all other parameters we get circle graphs, well known to be polynomially recognizable." @default.
- W4226148049 created "2022-05-05" @default.
- W4226148049 creator A5014039487 @default.
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- W4226148049 date "2021-12-22" @default.
- W4226148049 modified "2023-10-14" @default.
- W4226148049 title "Recognising the overlap graphs of subtrees of restricted trees is hard" @default.
- W4226148049 doi "https://doi.org/10.48550/arxiv.2202.01678" @default.
- W4226148049 hasPublicationYear "2021" @default.
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