2026-07-24T02:22:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:21081 2024-09-23T09:13:16Z ddc:004 open_access

Sparse Outerstring Graphs Have Logarithmic Treewidth An, Shinwoo Oh, Eunjin Xue, Jie Outerstring graphs geometric intersection graphs treewidth An outerstring graph is the intersection graph of curves lying inside a disk with one endpoint on the boundary of the disk. We show that an outerstring graph with n vertices has treewidth O(αlog n), where α denotes the arboricity of the graph, with an almost matching lower bound of Ω(α log (n/α)). As a corollary, we show that a t-biclique-free outerstring graph has treewidth O(t(log t)log n). This leads to polynomial-time algorithms for most of the central NP-complete problems such as Independent Set, Vertex Cover, Dominating Set, Feedback Vertex Set, Coloring for sparse outerstring graphs. Also, we can obtain subexponential-time (exact, parameterized, and approximation) algorithms for various NP-complete problems such as Vertex Cover, Feedback Vertex Set and Cycle Packing for (not necessarily sparse) outerstring graphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shinwoo An and Eunjin Oh and Jie Xue 2024 Is Part Of LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2024.10 urn:nbn:de:0030-drops-210816 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.10 eng https://creativecommons.org/licenses/by/4.0/legalcode