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 -