Bidimensionality of geometric intersection graphs

A. Grigoriev*, A. Koutsonas, D.M. Thilikos

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

2 Citations (Web of Science)

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.
Original languageEnglish
Title of host publicationSOFSEM 2014: Theory and Practice of Computer Science
EditorsV. Geffert, B. Preneel, B. Rovan, J. Stuller, A. Min Tjoa
Place of PublicationSwitzerland
PublisherSpringer
Pages293-305
Number of pages13
ISBN (Print)978-3-319-04297-8
DOIs
Publication statusPublished - 1 Jan 2014
Event40th International Conference on Current Trends in Theory and Practice of Computer Science - Novy Smokovec, Slovakia
Duration: 26 Jan 201429 Jan 2014

Publication series

SeriesLecture Notes in Computer Science
Volume8327

Conference

Conference40th International Conference on Current Trends in Theory and Practice of Computer Science
Country/TerritorySlovakia
CityNovy Smokovec
Period26/01/1429/01/14

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