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- W4384263588 abstract "Twin-width is a width parameter introduced by Bonnet, Kim, Thomass'e and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. We prove that the twin-width of every graph embeddable in a surface of Euler genus $g$ is $18sqrt{47g}+O(1)$, which is asymptotically best possible as it asymptotically differs from the lower bound by a constant multiplicative factor. Our proof also yields a quadratic time algorithm to find a corresponding contraction sequence. To prove the upper bound on twin-width of graphs embeddable in surfaces, we provide a stronger version of the Product Structure Theorem for graphs of Euler genus $g$ that asserts that every such graph is a subgraph of the strong product of a path and a graph with a tree-decomposition with all bags of size at most eight with a single exceptional bag of size $max{8,32g-27}$." @default.
- W4384263588 created "2023-07-14" @default.
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- W4384263588 date "2023-07-11" @default.
- W4384263588 modified "2023-09-27" @default.
- W4384263588 title "Twin-width of graphs on surfaces" @default.
- W4384263588 doi "https://doi.org/10.48550/arxiv.2307.05811" @default.
- W4384263588 hasPublicationYear "2023" @default.
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