TY - GEN

T1 - Bidimensionality of geometric intersection graphs

AU - Grigoriev, Alexander

AU - Koutsonas, Athanassios

AU - Thilikos, Dimitrios M.

PY - 2014

Y1 - 2014

N2 - Let 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 where each body of the collection is represented by a vertex, and two vertices of 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.

AB - Let 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 where each body of the collection is represented by a vertex, and two vertices of 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.

KW - bidimensionality

KW - geometric intersection graphs

KW - grid exlusion theorem

UR - http://www.scopus.com/inward/record.url?scp=84958524606&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-04298-5_26

DO - 10.1007/978-3-319-04298-5_26

M3 - Conference contribution

AN - SCOPUS:84958524606

SN - 9783319042978

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 293

EP - 305

BT - SOFSEM 2014

PB - Springer Verlag

T2 - 40th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2014

Y2 - 26 January 2014 through 29 January 2014

ER -