eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-23
66:1
66:15
10.4230/LIPIcs.MFCS.2024.66
article
Twin-Width of Graphs on Surfaces
Kráľ, Daniel
1
https://orcid.org/0000-0001-8680-0890
Pekárková, Kristýna
1
https://orcid.org/0000-0003-3539-6431
Štorgel, Kenny
2
https://orcid.org/0000-0002-1772-7404
Faculty of Informatics, Masaryk University, Brno, Czech Republic
Faculty of Information Studies in Novo mesto, Slovenia
Twin-width is a width parameter introduced by Bonnet, Kim, Thomassé and Watrigant [FOCS'20, JACM'22], which has many structural and algorithmic applications. Hliněný and Jedelský [ICALP'23] showed that every planar graph has twin-width at most 8. We prove that the twin-width of every graph embeddable in a surface of Euler genus g is at most 18√{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{6, 32g-37}.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol306-mfcs2024/LIPIcs.MFCS.2024.66/LIPIcs.MFCS.2024.66.pdf
twin-width
graphs on surfaces
fixed parameter tractability