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Bidimensionality of Geometric Intersection Graphs

Alexander Grigoriev 1 Athanassios Koutsonas 2 Dimitrios M. Thilikos 3, 2 
3 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the corresponding bodies is non-empty. For such graph classes and under natural restrictions on their maximum degree or subgraph exclusion, we prove that the relation between their treewidth and the maximum size of a grid minor is linear. These combinatorial results vastly extend the applicability of all the meta-algorithmic results of the bidimensionality theory to geometrically defined graph classes.
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Submitted on : Thursday, November 14, 2013 - 4:16:36 PM
Last modification on : Friday, August 5, 2022 - 3:02:53 PM

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Alexander Grigoriev, Athanassios Koutsonas, Dimitrios M. Thilikos. Bidimensionality of Geometric Intersection Graphs. SOFSEM: Theory and Practice of Computer Science, Jan 2014, Špindlerův Mlýn, Czech Republic. pp.293-305, ⟨10.1007/978-3-319-04298-5_26⟩. ⟨lirmm-00904537⟩



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