Abstract
Let \({\cal B}\) 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 \(G_{\cal B}\) where each body of the collection \({\cal B}\) is represented by a vertex, and two vertices of \(G_{\cal B}\) 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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Grigoriev, A., Koutsonas, A., Thilikos, D.M. (2014). Bidimensionality of Geometric Intersection Graphs. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_26
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DOI: https://doi.org/10.1007/978-3-319-04298-5_26
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